A322975 Number of divisors d of n such that d-2 is prime.

0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 2, 0, 1, 2, 2, 0, 2, 1, 1, 4, 0, 0, 1, 2, 2, 0, 2, 0, 1, 2, 2, 1, 0, 0, 3, 1, 1, 4, 1, 2, 1, 0, 1, 1, 2, 0, 2, 1, 0, 4, 2, 1, 2, 0, 2, 2, 0, 0, 3, 2, 1, 0, 1, 0, 4, 3, 1, 1, 0, 2, 1, 0, 2, 3, 3, 0, 0, 1, 2, 5

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 subtracted from each, as 1-2 = -1, 3-2 = 1, 5-2 = 3, etc, the only differences that are primes are: [3, 5, 7, 13, 19, 31, 43, 53, 61, 97, 103, 163, 229, 313, 383, 691, 1153, 1483, 3463], thus (a10395) = 19.
		

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, A062301, A067513, A072627, A322358, A322976, A322977, A322978.

Programs

Mathematica

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

PARI

A322975(n) = sumdiv(n, d, isprime(d-2));

Formula

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

a(A000040(n)) = A062301(n).