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

Author

Amiram Eldar, Sep 27 2017

Keywords

• nonn

Comments

Analogous to abundant numbers (A005101) with bi-unitary sigma (A188999) instead of sigma (A000203).

Examples

			24 is in the sequence since bsigma(24) = 60 > 2*24.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101, A034683, A188999.

Programs

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 *)

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