A027759 - OEIS

%I #23 May 26 2021 03:06:19

%S 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,

%T 5,1,929,1,15745,1,557,1,5,1,2557843,1,5,1,15541,1,1805,1,743,1,241,1,

%U 60887,1,61,1,1673,1,821,1,929,1,301,1,79085411,1,5,1,557

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

%H John Cerkan, <a href="/A027759/b027759.txt">Table of n, a(n) for n = 1..10000</a>

%F a(2n-1) = 1 and a(2n) = A000146(n)* A002445(n) - A000367(n) for n > 0. - _Thomas Ordowski_, May 06 2021

%e 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, ...

%t a[n_] := 1/(Select[Divisors[n], PrimeQ[# + 1]&] + 1) // Total // Numerator;

%t Array[a, 100] (* _Jean-François Alcover_, Sep 20 2020 *)

%o (PARI) a(n) = numerator(sumdiv(n, d, if (isprime(d+1), 1/(d+1)))); \\ _Michel Marcus_, May 06 2021

%Y Cf. A027760 (denominator).

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_.

%E a(57)-a(64) from _John Cerkan_, Mar 21 2018