A069235 Numbers k, not perfect squares, such that the squarefree part of k divides sigma(k).

6, 24, 28, 40, 54, 96, 117, 120, 135, 147, 150, 216, 224, 234, 252, 270, 294, 360, 384, 468, 486, 496, 507, 540, 588, 600, 640, 672, 700, 726, 775, 819, 847, 864, 891, 931, 936, 1000, 1014, 1080, 1083, 1176, 1323, 1350, 1372, 1536, 1550, 1638, 1694, 1734

Offset: 1

Author

Benoit Cloitre, Apr 13 2002

Keywords

• easy
• nonn

Examples

			54 is not a square, sigma(54)=120, 6 is the squarefree part of 54 and 6 divides 120. Hence a(5)=54 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Crossrefs

Cf. A000037 (nonsquares), A000203, A007913.

Programs

Mathematica

f[p_, e_] := p^Mod[e, 2]; sqfp[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[2000], (s = sqfp[#]) > 1 && Divisible[DivisorSigma[1, #], s] &] (* Amiram Eldar, May 10 2022 *)

PARI

c=0; for(n=2, 244783, if(issquare(n)==0, if(sigma(n)%core(n)==0, c++; write("b069235.txt", c " " n)))) /* Donovan Johnson, Aug 18 2013 */