login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of even divisors d of 2n such that d-1 is prime.
4

%I #10 Jan 04 2019 17:36:50

%S 0,1,1,2,0,3,1,2,2,2,0,5,0,2,2,3,0,4,1,3,3,2,0,6,0,1,3,3,0,6,1,3,1,2,

%T 1,7,1,2,1,4,0,6,0,3,4,1,0,7,2,2,2,3,0,6,1,3,3,1,0,8,0,2,4,4,0,5,0,3,

%U 2,4,0,8,0,2,3,4,1,3,1,5,3,2,0,9,0,1,2,3,0,9,2,2,2,1,1,8,1,3,3,4,0,5,0,3,4

%N Number of even divisors d of 2n such that d-1 is prime.

%H Antti Karttunen, <a href="/A322978/b322978.txt">Table of n, a(n) for n = 1..15120</a>

%H Antti Karttunen, <a href="/A322978/a322978.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F a(n) = A322977(2*n).

%F a(n) = Sum_{d|(2*n), d>1} A059841(d)*A010051(d-1).

%t Array[DivisorSum[2 #, 1 &, And[EvenQ@ #, PrimeQ[# - 1]] &] &, 105] (* _Michael De Vlieger_, Jan 04 2019 *)

%o (PARI) A322978(n) = sumdiv(n+n, d, (!(d%2))*isprime(d-1));

%o (PARI)

%o A322977(n) = sumdiv(n, d, (!(d%2))*isprime(d-1));

%o A322978(n) = A322977(n+n);

%Y Cf. A010051, A059841.

%Y Bisection of A322977.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jan 04 2019