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A322977 Number of even divisors d of n such that d-1 is prime.

%I A322977 #11 Jan 04 2019 17:36:41
%S A322977 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 A322977 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 A322977 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 A322977 Number of even divisors d of n such that d-1 is prime.
%C A322977 Equally: Number of divisors d of n such that d-1 is an odd prime.
%H A322977 Antti Karttunen, <a href="/A322977/b322977.txt">Table of n, a(n) for n = 1..15120</a>
%H A322977 Antti Karttunen, <a href="/A322977/a322977.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A322977 a(n) = Sum_{d|n, d>1} A059841(d)*A010051(d-1).
%F A322977 a(n) <= A183063(n).
%t A322977 Array[DivisorSum[#, 1 &, And[EvenQ@ #, PrimeQ[# - 1]] &] &, 105] (* _Michael De Vlieger_, Jan 04 2019 *)
%o A322977 (PARI) A322977(n) = sumdiv(n, d, (!(d%2))*isprime(d-1));
%Y A322977 Cf. A010051, A059841, A072627, A183063, A322975, A322976, A322978 (bisection).
%K A322977 nonn
%O A322977 1,8
%A A322977 _Antti Karttunen_, Jan 04 2019