%I #8 Mar 27 2015 18:10:35

%S 1,1,2,2,3,3,4,2,4,4,3,5,5,5,5,6,6,4,6,8,6,5,6,7,7,9,7,8,7,7,9,9,11,7,

%T 11,9,9,7,11,9,10,8,10,12,11,7,11,12,12,9,13,11,11,15,14,15,14,10,11,

%U 14,13,13,15,17,12,14,14,15,19,14,19,15,15,18,15,17,15,17,16,17,17,18,17

%N a(n) = number of ways of representing 2*prime(n) as the unordered sum of two primes.

%C 2*prime(n) = A100484(n), the n-th even semiprime.

%C a(n) = A071681(n) + 1. - _Reinhard Zumkeller_, Mar 27 2015

%H Reinhard Zumkeller, <a href="/A116619/b116619.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A045917(A100484(n)).

%e 2*prime(23) = 166 can be represented in 6 ways as the unordered sum of two primes: 166 = 3+163 = 17+149 = 29+137 = 53+113 = 59+107 = 83+83, so a(23) = 6.

%e 2*prime(54) = 502 can be represented in 15 ways as the unordered sum of two primes: 502 = 3+499 = 11+491 = 23+479 = 41+461 = 53+449 = 59+443 = 71+431 = 83+419 = 101+401 = 113+389 = 149+353 = 191+311 = 233+269 = 239+263 = 251+251, so a(54) = 15.

%o (PARI) {for(n=1,83,c=0;k=2*prime(n);forprime(p=2,prime(n),if(isprime(k-p),c++));print1(c,","))} - Klaus Brockhaus, Dec 23 2006

%o (Haskell)

%o a116619 = (+ 1) . a071681 -- _Reinhard Zumkeller_, Mar 27 2015

%Y Cf. A000040, A001358, A045917, A100484.

%Y Cf. A071681, A010051.

%K easy,nonn

%O 1,3

%A _Jonathan Vos Post_, Mar 14 2006

%E Edited, corrected and extended by _Klaus Brockhaus_, Dec 23 2006