A185288 Numbers n for which the terms of the multiplicative sequence {n^2/A049417(n)} are integers.

1, 6, 60, 90, 120, 180, 360, 540, 816, 840, 1080, 1740, 1980, 2280, 2520, 3060, 3960, 5712, 6120, 8280, 9540, 11880, 12240, 16920, 18360, 19260, 24480, 25296, 25560, 32760, 36720, 42840, 48960, 54672, 57240, 63700, 73440, 74256, 84360, 85680, 97920, 103320, 115560

Offset: 1

Author

Vladimir Shevelev, Feb 20 2011

Keywords

• nonn

Comments

The sequence contains all infinitary perfect numbers (see A007357).

Examples

			Let n=120. Its representation over distinct terms of A050376 is 2*3*4*5. Therefore A049417(n)=(2+1)*(3+1)*(4+1)*(5+1)=360. Since 360 is a divisor of 120^2, 120 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007357, A049417, A064380, A185079, A185088, A185098, A185373, A185383.

Programs

Mathematica

fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; aQ[n_] := Divisible[n^2, isigma[n]]; Select[Range[58000], aQ] (* Amiram Eldar, Jul 21 2019 *)

Extensions

More terms from Nathaniel Johnston, Mar 16 2011

More terms from Amiram Eldar, Jul 21 2019