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Number of even divisors d of n such that d-1 is prime.
6

%I #11 Jan 04 2019 17:36:41

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A322977/b322977.txt">Table of n, a(n) for n = 1..15120</a>

%H Antti Karttunen, <a href="/A322977/a322977.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

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

%F a(n) <= A183063(n).

%t Array[DivisorSum[#, 1 &, And[EvenQ@ #, PrimeQ[# - 1]] &] &, 105] (* _Michael De Vlieger_, Jan 04 2019 *)

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

%Y Cf. A010051, A059841, A072627, A183063, A322975, A322976, A322978 (bisection).

%K nonn

%O 1,8

%A _Antti Karttunen_, Jan 04 2019