cp's OEIS Frontend

A066961 Numbers k such that sigma(k) divides sigma(sigma(k)).

%I A066961 #55 Dec 10 2024 11:59:18
%S A066961 1,5,12,54,56,87,95,276,308,427,429,446,455,501,581,611,9120,9180,
%T A066961 9504,9720,9960,10296,10620,10740,10824,11070,11310,11480,11484,11556,
%U A066961 11628,11748,11934,11960,12024,12036,12072,12084,12376,12460,12510,12570
%N A066961 Numbers k such that sigma(k) divides sigma(sigma(k)).
%C A066961 Is this sequence finite?
%C A066961 These are numbers k such that sigma(k) is a multiply-perfect number (A007691). - _Ivan N. Ianakiev_, Sep 13 2016
%H A066961 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 A066961 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A066961 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A066961 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 A066961 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 A066961 Select[Range[30000], Divisible[DivisorSigma[1, DivisorSigma[1, #]], DivisorSigma[1, #]] &] (* _Ivan N. Ianakiev_, Sep 13 2016 *)
%o A066961 (PARI) isok(n) = my(s=sigma(n)); s && ((sigma(s) % s) == 0); \\ _Michel Marcus_, Sep 17 2016
%o A066961 (Magma) [n: n in [1..13000] | (SumOfDivisors(SumOfDivisors(n)) mod SumOfDivisors(n) eq 0)]; // _Vincenzo Librandi_, Sep 13 2016
%Y A066961 Cf. A000203, A051027.
%Y A066961 Subsequences: A323653 (intersection with A007691, or equally, with A019278), A353365 (where the quotient is a power of 2).
%K A066961 nonn
%O A066961 1,2
%A A066961 _Benoit Cloitre_, Jan 26 2002
%E A066961 More terms from _Lior Manor_, Feb 06 2002