A027759 Numerator of Sum_{p prime, p-1|n} 1/p.

1, 5, 1, 31, 1, 41, 1, 31, 1, 61, 1, 3421, 1, 5, 1, 557, 1, 821, 1, 371, 1, 121, 1, 3421, 1, 5, 1, 929, 1, 15745, 1, 557, 1, 5, 1, 2557843, 1, 5, 1, 15541, 1, 1805, 1, 743, 1, 241, 1, 60887, 1, 61, 1, 1673, 1, 821, 1, 929, 1, 301, 1, 79085411, 1, 5, 1, 557

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Examples

			1/2, 5/6, 1/2, 31/30, 1/2, 41/42, 1/2, 31/30, 1/2, 61/66, 1/2, 3421/2730, 1/2, 5/6, 1/2, 557/510, ...
		

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027760 (denominator).

Programs

Mathematica

a[n_] := 1/(Select[Divisors[n], PrimeQ[# + 1]&] + 1) // Total // Numerator;
Array[a, 100] (* Jean-François Alcover, Sep 20 2020 *)

PARI

a(n) = numerator(sumdiv(n, d, if (isprime(d+1), 1/(d+1)))); \\ Michel Marcus, May 06 2021

Formula

a(2n-1) = 1 and a(2n) = A000146(n)* A002445(n) - A000367(n) for n > 0. - Thomas Ordowski, May 06 2021

Extensions

a(57)-a(64) from John Cerkan, Mar 21 2018