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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
OFFSET
1,1
COMMENTS
Supersequence of A063906.
A combination of the notions of 2-hyperperfect numbers (A007593) and near-perfect numbers (A181595).
LINKS
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 06 2018
STATUS
approved