A066961 - OEIS

%I #52 Sep 08 2022 08:45:05

%S 1,5,12,54,56,87,95,276,308,427,429,446,455,501,581,611,9120,9180,

%T 9504,9720,9960,10296,10620,10740,10824,11070,11310,11480,11484,11556,

%U 11628,11748,11934,11960,12024,12036,12072,12084,12376,12460,12510,12570

%N Numbers k such that sigma(k) divides sigma(sigma(k)).

%C Is this sequence finite?

%C These are numbers k such that sigma(k) is a multiply-perfect number (A007691). - _Ivan N. Ianakiev_, Sep 13 2016

%H Antti Karttunen, <a href="/A066961/b066961.txt">Table of n, a(n) for n = 1..3718</a> (first 1000 terms from Harry J. Smith)

%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e 12 is in the sequence since sigma(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28 divides sigma(28) = 1 + 2 + 4 + 7 + 14 + 28 = 56. - _Michael B. Porter_, Sep 22 2016

%p with(numtheory): A066961:=n->`if`(sigma(sigma(n)) mod sigma(n) = 0, n, NULL): seq(A066961(n), n=1..2*10^4); # _Wesley Ivan Hurt_, Sep 22 2016

%t Select[Range[30000], Divisible[DivisorSigma[1, DivisorSigma[1, #]], DivisorSigma[1, #]] &] (* _Ivan N. Ianakiev_, Sep 13 2016 *)

%o (PARI) { n=0; for (m=1, 10^10, if (sigma(sigma(m)) % sigma(m) == 0, write("b066961.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Apr 11 2010

%o (PARI) isok(n) = (s=sigma(n)) && ((sigma(s) % s) == 0); \\ _Michel Marcus_, Sep 17 2016

%o (Magma) [n: n in [1..13000] | (SumOfDivisors(SumOfDivisors(n)) mod SumOfDivisors(n) eq 0)]; // _Vincenzo Librandi_, Sep 13 2016

%Y Cf. A000203, A051027.

%Y Subsequences: A323653 (intersection with A007691, or equally, with A019278), A353365 (where the quotient is a power of 2).

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jan 26 2002

%E More terms from _Lior Manor_, Feb 06 2002