A116619 a(n) = number of ways of representing 2*prime(n) as the unordered sum of two primes.

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

Offset: 1

Author

Jonathan Vos Post, Mar 14 2006

Keywords

• easy
• nonn

Comments

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

a(n) = A071681(n) + 1. - Reinhard Zumkeller, Mar 27 2015

Examples

			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.
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.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A045917, A100484.

Cf. A071681, A010051.

Programs

Haskell

a116619 = (+ 1) . a071681  -- Reinhard Zumkeller, Mar 27 2015

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

Formula

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

Extensions

Edited, corrected and extended by Klaus Brockhaus, Dec 23 2006