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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). 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Analogous to abundant numbers (A005101) with bi-unitary sigma (A188999) instead of sigma (A000203). LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 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 Cf. A005101, A034683, A188999. Sequence in context: A290451 A068544 A284174 * A334972 A109797 A129656 Adjacent sequences:  A292979 A292980 A292981 * A292983 A292984 A292985 KEYWORD nonn AUTHOR Amiram Eldar, Sep 27 2017 STATUS approved

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Last modified April 12 10:06 EDT 2021. Contains 342920 sequences. (Running on oeis4.)