A326715 - OEIS

%I #16 Dec 15 2020 18:32:27

%S 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 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,

%U 179,181,191,193,197,199,211,223,227,229,233,239,241

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

%C 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 Robert Israel, <a href="/A326715/b326715.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Giuga_number">Giuga number</a>

%F n such that A326690(n) = 1.

%e 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 filter:= proc(n) local p;

%p    denom(add(1/p, p = numtheory:-factorset(n))-1/n)=1

%p end proc:

%p select(filter, [$1..300]); # _Robert Israel_, Dec 15 2020

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

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

%t Select[Range[148], f[#] == 1 &]

%Y Cf. A007850, A326689, A326690, A326691, A326692.

%K nonn

%O 1,2

%A _Jonathan Sondow_, Jul 20 2019