

A116619


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


5



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
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OFFSET

1,3


COMMENTS

2*prime(n) = A100484(n), the nth even semiprime.
a(n) = A071681(n) + 1.  Reinhard Zumkeller, Mar 27 2015


LINKS

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


FORMULA

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


EXAMPLE

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.


PROG

(PARI) {for(n=1, 83, c=0; k=2*prime(n); forprime(p=2, prime(n), if(isprime(kp), c++)); print1(c, ", "))}  Klaus Brockhaus, Dec 23 2006
(Haskell)
a116619 = (+ 1) . a071681  Reinhard Zumkeller, Mar 27 2015


CROSSREFS

Cf. A000040, A001358, A045917, A100484.
Cf. A071681, A010051.
Sequence in context: A106494 A339811 A015135 * A337776 A091220 A057955
Adjacent sequences: A116616 A116617 A116618 * A116620 A116621 A116622


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Mar 14 2006


EXTENSIONS

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


STATUS

approved



