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%I #22 Dec 04 2021 12:29:38
%S 1,2,3,1,5,2,7,1,1,2,11,3,13,2,1,1,17,2,19,1,3,2,23,1,1,2,1,1,29,30,
%T 31,1,1,2,1,1,37,2,3,1,41,2,43,1,1,2,47,3,1,2,1,1,53,2,5,7,3,2,59,1,
%U 61,2,1,1,1,6,67,1,1,2,71,1,73,2,3,1,1,2,79
%N a(n) = n/denominator(Sum_{prime p | n} 1/p - 1/n).
%C Denominator(Sum_{prime p | n} 1/p - 1/n) is a factor of n, since all primes in the sum divide n. So a(n) is an integer.
%H Antti Karttunen, <a href="/A326691/b326691.txt">Table of n, a(n) for n = 1..20000</a>
%H Christian Krause, et al, <a href="https://github.com/loda-lang">LODA, an assembly language, a computational model and a tool for mining integer sequences</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Giuga_number">Giuga number</a>
%F a(n) = n/A326690(n).
%F a(n) = n > 1 iff n is either a prime or a Giuga number A007850.
%F a(n) = gcd(n, 1+((n-1)*A003415(n))). [Conjectured, after an empirical formula found by LODA miner. This holds at least up to n=2^27] - _Antti Karttunen_, Mar 15 2021
%e a(18) = 18/denominator(Sum_{prime p | 18} 1/p - 1/18) = 18/denominator(1/2 + 1/3 - 1/18) = 18/denominator(7/9) = 18/9 = 2.
%e a(30) = 30/denominator(Sum_{prime p | 30} 1/p - 1/30) = 30/denominator(1/2 + 1/3 + 1/5 - 1/30) = 30/denominator(1/1) = 30/1 = 30, and 30 is a Giuga number.
%t PrimeFactors[n_] := Select[Divisors[n], PrimeQ];
%t f[n_] := Denominator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];
%t Table[n/f[n], {n, 79}]
%o (PARI) A326691(n) = (n/A326690(n)); \\ _Antti Karttunen_, Mar 15 2021
%Y Cf. A003415, A007850, A326689, A326690, A326692, A326715.
%K nonn
%O 1,2
%A _Jonathan Sondow_, Jul 20 2019
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