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A292982
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Bi-unitary abundant numbers: numbers n such that bsigma(n) > 2n, where bsigma is the sum of the bi-unitary divisors function (A188999).
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15
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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
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OFFSET
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1,1
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COMMENTS
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Analogous to abundant numbers (A005101) with bi-unitary sigma (A188999) instead of sigma (A000203).
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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24 is in the sequence since bsigma(24) = 60 > 2*24.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A005101, A034683, A188999.
Sequence in context: A290451 A068544 A284174 * A334972 A109797 A129656
Adjacent sequences: A292979 A292980 A292981 * A292983 A292984 A292985
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KEYWORD
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nonn
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AUTHOR
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Amiram Eldar, Sep 27 2017
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STATUS
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approved
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