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A306984
Infinitary weird numbers: infinitary abundant numbers (A129656) that are not infinitary pseudoperfect numbers (A306983).
8
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 18 2019
STATUS
approved