A306987 Primitive abundant numbers (A071395) that are pseudoperfect (A005835).

20, 88, 104, 272, 304, 368, 464, 550, 572, 650, 748, 945, 1184, 1312, 1376, 1430, 1504, 1575, 1696, 1870, 1888, 1952, 2002, 2090, 2205, 2210, 2470, 2530, 2584, 2990, 3128, 3190, 3230, 3410, 3465, 3496, 3770, 3944, 4070, 4095, 4216, 4288, 4408, 4510, 4544, 4672

Offset

1,1

Comments

By definition these numbers are also primitive pseudoperfect (A006036).

Benkoski and Erdős proved that this sequence is infinite, since it includes all the numbers of the form 2^k * p with p a prime such that 2^k < p < 2^(k+1).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

S. J. Benkoski and P. Erdős, On weird and pseudoperfect numbers, Math. Comp. 28 (1974), 617-623. Corrigendum: Math. Comp. 29 (1975), 673-674.

Mathematica

paQ[n_]:=DivisorSigma[1, n] > 2n && Times @@ Boole@ Map[DivisorSigma[1, #] < 2 # &, Most@ Divisors@ n] == 1; psQ[n_]:=Module[{d= Most[Divisors[n] ]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] > 0]; Select[Range[5000], paQ[#]&&psQ[#]&] (* after Michael De Vlieger at A071395 and T. D. Noe at A005835 *)

Crossrefs

Cf. A005835, A006036, A071395.

Sequence in context: A243645 A219824 A339343 * A249983 A234258 A213839

Adjacent sequences: A306984 A306985 A306986 * A306988 A306989 A306990

Keyword

nonn

Author

Amiram Eldar, Mar 18 2019

Status

approved