OFFSET
1,2
COMMENTS
Any prime power p^k with k > 1 is a term, as 1/p - 1/p^k = (p^(k-1) - 1)/p^k which is in reduced form and has denominator p^k.
Are there infinitely many Carmichael numbers A002997 in the sequence?
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1/3 + 1/5 - 1/15 = 7/15 has denominator 15, so 15 is a term.
MATHEMATICA
PrimeFactors[n_] := Select[Divisors[n], PrimeQ];
f[n_] := Denominator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];
Select[Range[148], f[#] == # &]
PROG
(PARI) is(k) = {my(p = factor(k)[, 1]); denominator(sum(i = 1, #p, 1/p[i]) - 1/k) == k; } \\ Amiram Eldar, Apr 26 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Jul 20 2019
STATUS
approved