A322976 Number of divisors d of n such that d+2 is prime.

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

Offset: 1

Author

Antti Karttunen, Jan 04 2019

Keywords

• nonn

Examples

			10395 has 32 divisors: [1, 3, 5, 7, 9, 11, 15, 21, 27, 33, 35, 45, 55, 63, 77, 99, 105, 135, 165, 189, 231, 297, 315, 385, 495, 693, 945, 1155, 1485, 2079, 3465, 10395]. When 2 is added to each, as 1+2 = 3, 3+2 = 5, 5+2 = 7, etc, the only sums that are primes are: [3, 5, 7, 11, 13, 17, 23, 29, 37, 47, 79, 101, 107, 137, 167, 191, 233, 317, 947, 1487, 2081, 3467], thus (a10395) = 22.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10395
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A010051, A067513, A072627, A100821, A322358, A322975, A322977, A322978.

Programs

Mathematica

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

PARI

A322976(n) = sumdiv(n, d, isprime(d+2));

Formula

a(n) = Sum_{d|n} A010051(d+2).

a(A000040(n)) = 1 + A100821(n).