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A305818 Number of proper divisors d of n such that 2d+1 is a prime. 3

%I #7 Jun 15 2018 09:26:21

%S 0,1,1,2,1,3,1,2,2,3,1,4,1,2,3,3,1,5,1,3,2,3,1,5,2,2,3,3,1,6,1,3,3,2,

%T 2,6,1,2,2,5,1,6,1,3,5,3,1,5,1,3,2,3,1,6,3,4,2,3,1,8,1,2,4,3,2,6,1,2,

%U 3,5,1,8,1,2,4,2,2,6,1,5,3,3,1,6,2,2,3,5,1,9,1,3,2,2,2,6,1,3,5,5,1,5,1,4,6

%N Number of proper divisors d of n such that 2d+1 is a prime.

%C Number of terms of A005097 which are less than n that divide n.

%H Antti Karttunen, <a href="/A305818/b305818.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n, d<n} A101264(d).

%F a(n) = A086668(n) - A101264(n).

%o (PARI) A305818(n) = sumdiv(n, d, (d<n)*isprime(d+d+1));

%Y Cf. A005097, A086668, A101264.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 15 2018

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