A322978 Number of even divisors d of 2n such that d-1 is prime.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 04 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..15120
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A010051, A059841.

Bisection of A322977.

Programs

Mathematica

Array[DivisorSum[2 #, 1 &, And[EvenQ@ #, PrimeQ[# - 1]] &] &, 105] (* Michael De Vlieger, Jan 04 2019 *)

PARI

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

PARI

A322977(n) = sumdiv(n, d, (!(d%2))*isprime(d-1));
A322978(n) = A322977(n+n);

Formula

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

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