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Most/some third-party lenses report better apertures than they actually have - e.g. with f/6.3, the Sigma 150-600mm f5-6.3 Contemporary DG OS HSM would no longer work in AF-mode _{(or, to be more exact, the 1300D would deactivate AF)} :

[If] the maximum aperture becomes higher than f/5.6, AF shooting will not be possible (except in FlexiZone - Single and Live mode during Live View shooting).

^{See p. 100 in your camera's manual}

As a workaround, such lenses often report 5.6 as maximum aperture - so AF will still work. Most of the time, it is somewhat slower than the AF of a real f/5.6-lens.

This does not explain the f/4.5 at 150mm, though. My guess would be that it is easier to shift the whole max-aperture-value down than to just "correct" it for values above f/5.6.

On a side-note: If the Sigma lens really was f/4.5-5.6, they would definitely sell it as such, as larger apertures usually sell better (and at a higher price).

Most/some third-party lenses report better apertures than they actually have - e.g. with f/6.3, the Sigma 150-600mm f5-6.3 Contemporary DG OS HSM would no longer work with phase-detection-AF _{(or, to be more exact, the 1300D, as most entry- and mid-range-models, would deactivate PDAF)} :

[If] the maximum aperture becomes higher than f/5.6, AF shooting will not be possible (except in FlexiZone - Single and Live mode during Live View shooting).

^{See p. 100 in your camera's manual}

As you can see, contrast-detection-AF (as used in Live View) would still work - and it would not stop, ever, as long as it has enough light to work.

As a workaround, such lenses often report 5.6 as maximum aperture - so AF will still work. Most of the time, it is somewhat slower than the AF of a real f/5.6-lens.

This does not explain the f/4.5 at 150mm, though. My guess would be that it is easier to shift the whole max-aperture-value down than to just "correct" it for values above f/5.6.

On a side-note: If the Sigma lens really was f/4.5-5.6, they would definitely sell it as such, as larger apertures usually sell better (and at a higher price).

Most/some third-party lenses report better apertures than they actually have - e.g. with f/6.3, the Sigma 150-600mm f5-6.3 Contemporary DG OS HSM would no longer work in AF-ode _{(or, to be more exact, the 1300D would deactivate AF)} :

[If] the maximum aperture becomes higher than f/5.6, AF shooting will not be possible (except in FlexiZone - Single and Live mode during Live View shooting).

^{See p. 100 in your camera's manual}

As a workaround, such lenses often report 5.6 as maximum aperture - so AF will still work. Most of the time, it is somewhat slower than the AF of a real f/5.6-lens.

This does not explain the f/4.5 at 150mm, though. My guess would be that it is easier to shift the whole max-aperture-value down than to just "correct" it for values above f/5.6.

On a side-note: If the Sigma lens really was f/4.5-5.6, they would definitely sell it as such, as larger apertures usually sell better (and at a higher price).

Most/some third-party lenses report better apertures than they actually have - e.g. with f/6.3, the Sigma 150-600mm f5-6.3 Contemporary DG OS HSM would no longer work in AF-mode _{(or, to be more exact, the 1300D would deactivate AF)} :

[If] the maximum aperture becomes higher than f/5.6, AF shooting will not be possible (except in FlexiZone - Single and Live mode during Live View shooting).

^{See p. 100 in your camera's manual}

As a workaround, such lenses often report 5.6 as maximum aperture - so AF will still work. Most of the time, it is somewhat slower than the AF of a real f/5.6-lens.

This does not explain the f/4.5 at 150mm, though. My guess would be that it is easier to shift the whole max-aperture-value down than to just "correct" it for values above f/5.6.

On a side-note: If the Sigma lens really was f/4.5-5.6, they would definitely sell it as such, as larger apertures usually sell better (and at a higher price).

Most/some third-party lenses report better apertures than they actually have - e.g. with f/6.3, the Sigma 150-600mm f5-6.3 Contemporary DG OS HSM would no longer work in AF-ode _{(or, to be more exact, the 1300D would deactivate AF)} :

[If] the maximum aperture becomes higher than f/5.6, AF shooting will not be possible (except in FlexiZone - Single and Live mode during Live View shooting).

^{See p. 100 in your camera's manual}

As a workaround, such lenses often report 5.6 as maximum aperture - so AF will still work. Most of the time, it is somewhat slower than the AF of a real f/5.6-lens.

This does not explain the f/4.5 at 150mm, though. My guess would be that it is easier to shift the whole max-aperture-value down than to just "correct" it for values above f/5.6.

Most/some third-party lenses report better apertures than they actually have - e.g. with f/6.3, the Sigma 150-600mm f5-6.3 Contemporary DG OS HSM would no longer work in AF-ode _{(or, to be more exact, the 1300D would deactivate AF)} :

[If] the maximum aperture becomes higher than f/5.6, AF shooting will not be possible (except in FlexiZone - Single and Live mode during Live View shooting).

^{See p. 100 in your camera's manual}

As a workaround, such lenses often report 5.6 as maximum aperture - so AF will still work. Most of the time, it is somewhat slower than the AF of a real f/5.6-lens.

This does not explain the f/4.5 at 150mm, though. My guess would be that it is easier to shift the whole max-aperture-value down than to just "correct" it for values above f/5.6.

On a side-note: If the Sigma lens really was f/4.5-5.6, they would definitely sell it as such, as larger apertures usually sell better (and at a higher price).