A306984 Infinitary weird numbers: infinitary abundant numbers (A129656) that are not infinitary pseudoperfect numbers (A306983).

70, 4030, 5390, 5830, 7192, 7400, 7912, 9272, 10430, 10570, 10792, 10990, 11410, 11690, 11830, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17920, 17990, 18410, 18830, 18970, 19390, 19670

Offset

1,1

Comments

Differs from bi-unitary weird numbers from n >= 32 (a(32) = 17920 is not bi-unitary weird).

Links

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

Mathematica

idivs[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[ x ] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]] ; s = {}; Do[d = Most[idivs[n]]; If[Total[d]<n, Continue[]]; c = SeriesCoefficient[ Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c < 1, AppendTo[s, n]], {n, 2, 10000}]; s

Crossrefs

Cf. A006037, A049417, A064114, A126168, A129656, A292986, A321146, A306983.

Sequence in context: A227273 A298463 A275295 * A292986 A064114 A354281

Adjacent sequences: A306981 A306982 A306983 * A306985 A306986 A306987

Keyword

nonn

Author

Amiram Eldar, Mar 18 2019

Status

approved