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A326689
Numerator of the fraction (Sum_{prime p | n} 1/p - 1/n).
6
-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
1,6
COMMENTS
See Comments on denominators in A326690.
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).
EXAMPLE
-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
MATHEMATICA
PrimeFactors[n_] := Select[Divisors[n], PrimeQ];
g[n_] := Numerator[Sum[1/p, {p, PrimeFactors[n]}] - 1/n];
Table[ g[n], {n, 100}]
PROG
(PARI) a(n) = numerator(sumdiv(n, d, isprime(d)/d) - 1/n); \\ Michel Marcus, Jul 19 2019
CROSSREFS
Denominators are A326690. Cf. also A007850, A309132, A309235, A309378.
Cf. A028235.
Sequence in context: A152039 A180196 A317843 * A334861 A359674 A323248
KEYWORD
sign,frac
AUTHOR
Jonathan Sondow, Jul 18 2019
STATUS
approved