OFFSET
1,1
COMMENTS
Analogous to odd abundant numbers (A005231) with bi-unitary sigma (A188999) instead of sigma (A000203).
The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 1, 2, 82, 559, 6493, 61831, 642468, 6339347, 63112602, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00063... . - Amiram Eldar, Sep 02 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
945 is in the sequence since bsigma(945) = 1920 > 2*945.
MATHEMATICA
f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=
DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bOddAbundantQ[n_] := OddQ[n] && bsigma[n] > 2 n; Select[Range[1000], bOddAbundantQ] (* 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));
biusig(n) = vecsum(biudivs(n));
isok(n) = (n % 2) && (biusig(n) > 2*n); \\ Michel Marcus, Dec 15 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 01 2017
STATUS
approved