OFFSET
1,2
COMMENTS
A number m is a term if the sum of its bi-unitary divisors, A188999(m) divides the product of m by the number of its bi-unitary divisors A286324(m).
Numbers k whose harmonic mean of their bi-unitary divisors, A361782(k)/A361783(k), is an integer. - Amiram Eldar, Mar 24 2023
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..313 (all terms below 10^10, first 40 terms from Michel Marcus)
Jozsef Sandor, On bi-unitary harmonic numbers, arXiv:1105.0294 [math.NT], 2011. See pp. 13-20, but beware of typos and possible errors.
MATHEMATICA
f[p_, e_] := p^e * If[OddQ[e], (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2))]; bhQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; bhQ[1] = True; Select[Range[10^5], bhQ] (* Amiram Eldar, Mar 24 2023 *)
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) = my(v=biudivs(n)); denominator(n*#v/vecsum(v))==1;
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, May 07 2017
STATUS
approved