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

Author

Benoit Cloitre, Jan 26 2002

Keywords

• nonn

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

Examples

			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
		

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)

Crossrefs

Cf. A000203, A051027.

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

Programs

Magma

[n: n in [1..13000] | (SumOfDivisors(SumOfDivisors(n)) mod SumOfDivisors(n) eq 0)]; // Vincenzo Librandi, Sep 13 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 *)

PARI

isok(n) = my(s=sigma(n)); s && ((sigma(s) % s) == 0); \\ Michel Marcus, Sep 17 2016

Extensions

More terms from Lior Manor, Feb 06 2002