A069235 - OEIS

A069235

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

%I #19 May 10 2022 11:18:25

%S 6,24,28,40,54,96,117,120,135,147,150,216,224,234,252,270,294,360,384,

%T 468,486,496,507,540,588,600,640,672,700,726,775,819,847,864,891,931,

%U 936,1000,1014,1080,1083,1176,1323,1350,1372,1536,1550,1638,1694,1734

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

%H Amiram Eldar, <a href="/A069235/b069235.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Donovan Johnson)

%e 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.

%t 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 *)

%o (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 */

%Y Cf. A000037 (nonsquares), A000203, A007913.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 13 2002