cp's OEIS Frontend

A326692 Values of k for which the denominator of (Sum_{prime p | k} 1/p - 1/k) is k.

%I A326692 #12 Apr 26 2024 03:06:34
%S A326692 1,4,8,9,15,16,20,24,25,27,28,32,33,35,36,40,44,45,49,51,52,60,63,64,
%T A326692 65,68,69,72,76,77,81,85,87,88,91,92,95,96,99,100,104,108,112,115,116,
%U A326692 117,119,121,123,124,125,128,133,135,136,140,141,143,144,145,148
%N A326692 Values of k for which the denominator of (Sum_{prime p | k} 1/p - 1/k) is k.
%C A326692 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.
%C A326692 Are there infinitely many Carmichael numbers A002997 in the sequence?
%H A326692 Amiram Eldar, <a href="/A326692/b326692.txt">Table of n, a(n) for n = 1..10000</a>
%F A326692 Solutions of A326690(x) = x. That is, fixed points of A326690.
%e A326692 1/3 + 1/5 - 1/15 = 7/15 has denominator 15, so 15 is a term.
%t A326692 PrimeFactors[n_] := Select[Divisors[n], PrimeQ];
%t A326692 f[n_] := Denominator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];
%t A326692 Select[Range[148], f[#] == # &]
%o A326692 (PARI) is(k) = {my(p = factor(k)[,1]); denominator(sum(i = 1, #p, 1/p[i]) - 1/k) == k;} \\ _Amiram Eldar_, Apr 26 2024
%Y A326692 Cf. A002997, A326689, A326690, A326691, A326715.
%K A326692 nonn
%O A326692 1,2
%A A326692 _Jonathan Sondow_, Jul 20 2019