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A293186 Odd bi-unitary abundant numbers: odd numbers k such that bsigma(k) > 2*k, where bsigma is the sum of the bi-unitary divisors function (A188999). 6
945, 8505, 10395, 12285, 15015, 16065, 17955, 19305, 19635, 21735, 21945, 23205, 23625, 25245, 25515, 25935, 26565, 27405, 28215, 28875, 29295, 29835, 31185, 31395, 33345, 33495, 33915, 34125, 34155, 34965, 35805, 36855, 37125, 38745, 39585, 40635, 41055 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Analogous to odd abundant numbers (A005231) with bi-unitary sigma (A188999) instead of sigma (A000203).

LINKS

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

EXAMPLE

945 is in the sequence since bsigma(945) = 1920 > 2*945.

MATHEMATICA

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=

DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bOddAbundantQ[n_] := OddQ[n] && bsigma[n] > 2 n; Select[Range[1000], bOddAbundantQ] (* after Michael De Vlieger at A188999 *)

PROG

(PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }

gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));

biudivs(n) = select(x->(gcud(x, n/x)==1), divisors(n));

biusig(n) = vecsum(biudivs(n));

isok(n) = (n % 2) && (biusig(n) > 2*n); \\ Michel Marcus, Dec 15 2017

CROSSREFS

Cf. A005231, A129485, A188999, A292982.

Sequence in context: A109729 A294025 A275449 * A294027 A127666 A274756

Adjacent sequences:  A293183 A293184 A293185 * A293187 A293188 A293189

KEYWORD

nonn

AUTHOR

Amiram Eldar, Oct 01 2017

STATUS

approved

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Last modified May 28 16:25 EDT 2020. Contains 334684 sequences. (Running on oeis4.)