OFFSET
1,1
COMMENTS
Numbers k such that A099378(k) > k.
This sequence is infinite. For example, if p is a prime of the form 6*k-1, then p^2 is a term.
2 is the only prime term, since the denominator of the harmonic mean of the divisors of an odd prime p is (p+1)/2 < p.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
2 is a term since the harmonic mean of the divisors of 2 is 4/3 and 3 > 2.
4 is a term since the harmonic mean of the divisors of 4 is 12/7 and 7 > 4.
MATHEMATICA
q[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]] > n; Select[Range[2500], q]
PROG
(PARI) isok(k) = my(d=divisors(k)); (denominator(#d/sum(i=1, #d, 1/d[i])) > k); \\ Michel Marcus, Nov 01 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2021
STATUS
approved