A326689 Numerator of the fraction (Sum_{prime p | n} 1/p - 1/n).

-1, 0, 0, 1, 0, 2, 0, 3, 2, 3, 0, 3, 0, 4, 7, 7, 0, 7, 0, 13, 3, 6, 0, 19, 4, 7, 8, 17, 0, 1, 0, 15, 13, 9, 11, 29, 0, 10, 5, 27, 0, 20, 0, 25, 23, 12, 0, 13, 6, 17, 19, 29, 0, 22, 3, 5, 7, 15, 0, 61, 0, 16, 29, 31, 17, 10, 0, 37, 25, 29, 0, 59, 0, 19, 13, 41

Offset: 1

Author

Jonathan Sondow, Jul 18 2019

Keywords

• sign
• frac

Comments

See Comments on denominators in A326690.

Examples

			-1/1, 0/1, 0/1, 1/4, 0/1, 2/3, 0/1, 3/8, 2/9, 3/5, 0/1, 3/4, 0/1, 4/7, 7/15, 7/16, 0/1, 7/9, 0/1, 13/20, 3/7, 6/11, 0/1, 19/24, 4/25, 7/13, 8/27, 17/28, 0/1, 1/1
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Wikipedia, Giuga number

Crossrefs

Denominators are A326690. Cf. also A007850, A309132, A309235, A309378.

Cf. A028235.

Programs

Mathematica

PrimeFactors[n_] := Select[Divisors[n], PrimeQ];
g[n_] := Numerator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];
Table[ g[n], {n, 100}]

PARI

a(n) = numerator(sumdiv(n, d, isprime(d)/d) - 1/n); \\ Michel Marcus, Jul 19 2019

Formula

a(p) = 0 if p is a prime.

a(g) = 1 if g is a known Giuga number (see my 2nd comment in A007850).