A322976 - OEIS

%I #12 Jan 04 2019 17:36:30

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A322976/b322976.txt">Table of n, a(n) for n = 1..10395</a>

%H Antti Karttunen, <a href="/A322976/a322976.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

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

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

%e 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.

%t Array[DivisorSum[#, 1 &, PrimeQ[# + 2] &] &, 105] (* _Michael De Vlieger_, Jan 04 2019 *)

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

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

%K nonn

%O 1,3

%A _Antti Karttunen_, Jan 04 2019