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A326692 Values of n for which the denominator of (Sum_{prime p | n} 1/p - 1/n) is n. 3

%I #8 Jul 22 2019 06:31:40

%S 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 65,68,69,72,76,77,81,85,87,88,91,92,95,96,99,100,104,108,112,115,116,

%U 117,119,121,123,124,125,128,133,135,136,140,141,143,144,145,148

%N Values of n for which the denominator of (Sum_{prime p | n} 1/p - 1/n) is n.

%C 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 Are there infinitely many Carmichael numbers A002997 in the sequence?

%F Solutions of A326690(x) = x. That is, fixed points of A326690.

%e 1/3 + 1/5 - 1/15 = 7/15 has denominator 15, so 15 is a term.

%t PrimeFactors[n_] := Select[Divisors[n], PrimeQ];

%t f[n_] := Denominator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];

%t Select[Range[148], f[#] == # &]

%Y Cf. A002997, A326689, A326690, A326691, A326715.

%K nonn

%O 1,2

%A _Jonathan Sondow_, Jul 20 2019

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)