A056075 Numbers n such that n divides sigma(n) - d(n).

1, 4, 56, 7192, 7232, 7912, 10792, 17272, 30592, 114256, 2154584, 3428368, 44375136, 89245784, 2739393699744

Offset

1,2

Comments

Or, numbers n such that sigma(n) = k*n + d(n) for some k.

For most terms > 4, sigma(n) = 2*n + d(n), i.e., k=2. However, for the 12th term, k=3.

If p = 2^m-(2m+1) is prime and n = 2^(m-1)*p then sigma(n) = 2*n+d(n), i.e., k=2 and n is in the sequence. 56, 7232, 30592, 36028789368553472, 9223371897268338688 and 29230032746618058364071726105239688547563879792624 are such terms of the sequence. - Farideh Firoozbakht, Aug 19 2013

a(16) > 8*10^12. - Giovanni Resta, Nov 07 2019

Links

Table of n, a(n) for n=1..15.

Farideh Firoozbakht and M. F. Hasler, Variations on Euclid's formula for perfect numbers, Journal of Integer Sequences 13.3 (2010), 18 pp. Article ID 10.3.1.

Formula

Numbers n such that A000203(n) (mod n) == A000005(n) or A054024(n)=A000005(n). - Labos Elemer, Apr 12 2002

Mathematica

Do[If[Mod[DivisorSigma[1, n]-DivisorSigma[0, n], n]==0, Print[n]], {n, 1, 10^8}]

Prog

(PARI) is(n)=my(f=factor(n)); (sigma(f)-numdiv(f))%n==0 \\ Charles R Greathouse IV, Nov 04 2016

Crossrefs

Cf. A000203, A000005, A054024.

Sequence in context: A361217 A000573 A070019 * A000315 A080984 A071579

Adjacent sequences: A056072 A056073 A056074 * A056076 A056077 A056078

Keyword

nonn,more

Author

Robert G. Wilson v, Jul 26 2000

Extensions

a(15) from Giovanni Resta, Nov 07 2019

Status

approved