A292982 Bi-unitary abundant numbers: numbers n such that bsigma(n) > 2n, where bsigma is the sum of the bi-unitary divisors function (A188999).

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

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