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 A056075 Numbers n such that n divides sigma(n) - d(n). 4
 1, 4, 56, 7192, 7232, 7912, 10792, 17272, 30592, 114256, 2154584, 3428368, 44375136, 89245784 (list; graph; refs; listen; history; text; internal format)
 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 LINKS 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: A089516 A000573 A070019 * A000315 A080984 A071579 Adjacent sequences:  A056072 A056073 A056074 * A056076 A056077 A056078 KEYWORD nonn AUTHOR Robert G. Wilson v, Jul 26 2000 STATUS approved

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Last modified August 20 05:20 EDT 2018. Contains 313909 sequences. (Running on oeis4.)