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A326715 Values of n for which the denominator of (Sum_{prime p | n} 1/p - 1/n) is 1.

%I A326715 #16 Dec 15 2020 18:32:27
%S A326715 1,2,3,5,7,11,13,17,19,23,29,30,31,37,41,43,47,53,59,61,67,71,73,79,
%T A326715 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,
%U A326715 179,181,191,193,197,199,211,223,227,229,233,239,241
%N A326715 Values of n for which the denominator of (Sum_{prime p | n} 1/p - 1/n) is 1.
%C A326715 n is in the sequence iff either n = 1 or n is a prime or n is a Giuga number, by one definition of Giuga numbers A007850.
%H A326715 Robert Israel, <a href="/A326715/b326715.txt">Table of n, a(n) for n = 1..10000</a>
%H A326715 Wikipedia, <a href="https://en.wikipedia.org/wiki/Giuga_number">Giuga number</a>
%F A326715 n such that A326690(n) = 1.
%e A326715 a(30) = denominator(Sum_{prime p | 30} 1/p - 1/30) = denominator(1/2 + 1/3 + 1/5 - 1/30) = denominator(1/1) = 1, and 30 is a Giuga number.
%p A326715 filter:= proc(n) local p;
%p A326715    denom(add(1/p, p = numtheory:-factorset(n))-1/n)=1
%p A326715 end proc:
%p A326715 select(filter, [$1..300]); # _Robert Israel_, Dec 15 2020
%t A326715 PrimeFactors[n_] := Select[Divisors[n], PrimeQ];
%t A326715 f[n_] := Denominator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];
%t A326715 Select[Range[148], f[#] == 1 &]
%Y A326715 Cf. A007850, A326689, A326690, A326691, A326692.
%K A326715 nonn
%O A326715 1,2
%A A326715 _Jonathan Sondow_, Jul 20 2019