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A292982
Bi-unitary abundant numbers: numbers n such that bsigma(n) > 2n, where bsigma is the sum of the bi-unitary divisors function (A188999).
21
24, 30, 40, 42, 48, 54, 56, 66, 70, 72, 78, 80, 88, 96, 102, 104, 114, 120, 138, 150, 160, 162, 168, 174, 186, 192, 210, 216, 222, 224, 240, 246, 258, 264, 270, 280, 282, 288, 294, 312, 318, 320, 330, 336, 352, 354, 360, 366, 378, 384, 390, 402, 408, 416, 420
OFFSET
1,1
COMMENTS
Analogous to abundant numbers (A005101) with bi-unitary sigma (A188999) instead of sigma (A000203).
LINKS
EXAMPLE
24 is in the sequence since bsigma(24) = 60 > 2*24.
MATHEMATICA
f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=
DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bAbundantQ[n_] := bsigma[n] > 2 n; Select[Range[1000], bAbundantQ] (* 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));
isok(n) = vecsum(biudivs(n)) > 2*n; \\ Michel Marcus, Dec 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 27 2017
STATUS
approved