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

1, 5, 12, 54, 56, 87, 95, 276, 308, 427, 429, 446, 455, 501, 581, 611, 9120, 9180, 9504, 9720, 9960, 10296, 10620, 10740, 10824, 11070, 11310, 11480, 11484, 11556, 11628, 11748, 11934, 11960, 12024, 12036, 12072, 12084, 12376, 12460, 12510, 12570

Offset

1,2

Comments

Is this sequence finite?

These are numbers k such that sigma(k) is a multiply-perfect number (A007691). - Ivan N. Ianakiev, Sep 13 2016

Links

Antti Karttunen, Table of n, a(n) for n = 1..3718 (first 1000 terms from Harry J. Smith)

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Index entries for sequences related to sigma(n)

Example

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

Maple

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

Mathematica

Select[Range[30000], Divisible[DivisorSigma[1, DivisorSigma[1, #]], DivisorSigma[1, #]] &] (* Ivan N. Ianakiev, Sep 13 2016 *)

Prog

(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
(PARI) isok(n) = (s=sigma(n)) && ((sigma(s) % s) == 0); \\ Michel Marcus, Sep 17 2016
(Magma) [n: n in [1..13000] | (SumOfDivisors(SumOfDivisors(n)) mod SumOfDivisors(n) eq 0)]; // Vincenzo Librandi, Sep 13 2016

Crossrefs

Cf. A000203, A051027.

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

Sequence in context: A188118 A062978 A189421 * A179994 A131549 A342549

Adjacent sequences: A066958 A066959 A066960 * A066962 A066963 A066964

Keyword

nonn

Author

Benoit Cloitre, Jan 26 2002

Extensions

More terms from Lior Manor, Feb 06 2002

Status

approved