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

%I A322975 #11 Jan 04 2019 17:36:23
%S A322975 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,
%T A322975 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,
%U A322975 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
%N A322975 Number of divisors d of n such that d-2 is prime.
%H A322975 Antti Karttunen, <a href="/A322975/b322975.txt">Table of n, a(n) for n = 1..10395</a>
%H A322975 Antti Karttunen, <a href="/A322975/a322975.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322975 a(n) = Sum_{d|n, d>2} A010051(d-2).
%F A322975 a(A000040(n)) = A062301(n).
%e A322975 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.
%t A322975 Array[DivisorSum[#, 1 &, PrimeQ[# - 2] &] &, 105] (* _Michael De Vlieger_, Jan 04 2019 *)
%o A322975 (PARI) A322975(n) = sumdiv(n, d, isprime(d-2));
%Y A322975 Cf. A010051, A062301, A067513, A072627, A322358, A322976, A322977, A322978.
%K A322975 nonn
%O A322975 1,15
%A A322975 _Antti Karttunen_, Jan 04 2019