A292986 Bi-unitary weird numbers: bi-unitary abundant numbers (A292982) that are not bi-unitary pseudoperfect (A292985).

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, 17990, 18410, 18830, 18970, 19390, 19670, 19810

Offset

1,1

Comments

Analogous to weird numbers (A006037) with bi-unitary sigma (A188999) instead of sigma (A000203).

Links

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

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; bsigma[m_] := DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bAbundantQ[n_] := bsigma[n] > 2 n; a = {}; n = 0; While[Length[a] < 5, n++; If[!bAbundantQ[n], Continue[]]; d = Most[bdiv[n]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c <= 0, AppendTo[a, n]]]; a (* after T. D. Noe at A005835 and Michael De Vlieger at A188999 *)

Crossrefs

Cf. A006037, A064114, A188999, A292982, A292985.

Sequence in context: A298463 A275295 A306984 * A064114 A354281 A348631

Adjacent sequences: A292983 A292984 A292985 * A292987 A292988 A292989

Keyword

nonn

Author

Amiram Eldar, Sep 27 2017

Status

approved