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A305616 Near 2-hyperperfect numbers: numbers n such that sigma(n) - 3n/2 - 1/2 is a proper divisor of n. 1
15, 63, 147, 171, 207, 627, 663, 1023, 1647, 1971, 2975, 6399, 18063, 19359, 27639, 40215, 48895, 58563, 78819, 95511, 114231, 133595, 134871, 145915, 147455, 163539, 168507, 172287, 188067, 529983, 680859, 795639, 1207359, 1238571, 1553499, 1588491, 2049219 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Supersequence of A063906.

A combination of the notions of 2-hyperperfect numbers (A007593) and near-perfect numbers (A181595).

LINKS

Table of n, a(n) for n=1..37.

Bhabesh Das and Helen K. Saikia, Identities for Near and Deficient Hyperperfect Numbers, Indian Journal in Number Theory, Vol. 3 (2016), pp. 124-134, alternative link.

EXAMPLE

15 is in the sequence since sigma(15) = 24 and 24 - 3*15/2 - 1/2 = 1 is a proper divisor of 15.

MATHEMATICA

aQ[n_]:=Module[{d=DivisorSigma[1, n]-3n/2-1/2}, d>0 && d!=n && IntegerQ[d] && Divisible[n, d]]; Select[Range[1000000], aQ]

PROG

(PARI) isok(n) = (n % 2) && (k = sigma(n) - (3*n+1)/2) && (k>0) && !(n % k) && (k != n); \\ Michel Marcus, Jun 07 2018

CROSSREFS

Cf. A000203, A007593, A063906, A181595, A305617.

Sequence in context: A062965 A157968 A141759 * A104473 A135972 A138104

Adjacent sequences:  A305613 A305614 A305615 * A305617 A305618 A305619

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jun 06 2018

STATUS

approved

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Last modified February 24 09:40 EST 2020. Contains 332209 sequences. (Running on oeis4.)