A305616 Near 2-hyperperfect numbers: numbers n such that sigma(n) - 3n/2 - 1/2 is a proper divisor of n.

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

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: A157968 A141759 A335574 * A104473 A135972 A138104

Adjacent sequences: A305613 A305614 A305615 * A305617 A305618 A305619

Keyword

nonn

Author

Amiram Eldar, Jun 06 2018

Status

approved