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

1,1

Links

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

Example

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.

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 *)

Prog

(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 */

Crossrefs

Cf. A000037 (nonsquares), A000203, A007913.

Sequence in context: A349688 A273124 A349686 * A175200 A293453 A344754

Adjacent sequences: A069232 A069233 A069234 * A069236 A069237 A069238

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 13 2002

Status

approved