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%I #21 Apr 10 2018 08:24:14
%S 1,1,2,3,3,5,5,6,7,8,8,9,10,12,12,14,13,14,17,17,17,19,19,19,21,23,22,
%T 25,25,24,28,27,27,32,30,30,32,33,32,36,36,34,38,40,36,42,42,41,46,44,
%U 43,47,47,46,49,49,47,52,53,48,57,57,53,61,58,57,61,63,61,63
%N The number of partitions of 2n into exactly two parts such that the smaller and larger parts are not both prime.
%C Complement of A045917(n).
%H Vincenzo Librandi, <a href="/A227065/b227065.txt">Table of n, a(n) for n = 1..2000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = n - A045917(n).
%p A227065 := proc(n)
%p n-A045917(n) ;
%p end proc:
%p seq(A227065(n), n=1..100) ; # _R. J. Mathar_, Jul 01 2013
%t Table[n - Sum[(PrimePi[2 n - i] - PrimePi[2 n - i - 1]) (PrimePi[i] - PrimePi[i - 1]), {i, n}], {n, 100}] (* _Wesley Ivan Hurt_, Apr 07 2018 *)
%t f[n_]:=Length[Select[2 n - Prime[Range[PrimePi[n]]], PrimeQ]]; Table[n - f[n], {n, 100}] (* _Vincenzo Librandi_, Apr 10 2018 *)
%Y Cf. A045917.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Jun 30 2013
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