A322977 Number of even divisors d of n such that d-1 is prime.

0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 5, 0, 0, 0, 2, 0, 2, 0, 3, 0, 0, 0, 4, 0, 1, 0, 3, 0, 3, 0, 2, 0, 0, 0, 6, 0, 0, 0, 1, 0, 3, 0, 3, 0, 0, 0, 6, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 7, 0, 1, 0, 2, 0, 1, 0, 4, 0, 0, 0, 6, 0, 0, 0, 3, 0, 4, 0, 1, 0, 0, 0, 7, 0, 2, 0, 2, 0, 2, 0, 3, 0

Offset: 1

Author

Antti Karttunen, Jan 04 2019

Keywords

• nonn

Comments

Equally: Number of divisors d of n such that d-1 is an odd prime.

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, A072627, A183063, A322975, A322976, A322978 (bisection).

Programs

Mathematica

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

PARI

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

Formula

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

a(n) <= A183063(n).