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%I #44 Aug 05 2023 06:25:16
%S 0,0,0,0,1,1,1,2,2,2,3,3,4,5,5,5,6,7,7,8,8,8,9,9,10,11,11,12,13,13,13,
%T 14,15,15,16,16,16,17,18,18,19,19,20,21,21,22,23,24,24,25,25,25,26,26,
%U 26,27,27,28,29,30,31,32,33,33,34,34,35,36,36,36
%N a(n) = n - primepi(2n).
%C The number of distinct odd composite parts appearing in the partitions of 2n into two parts.
%C a(n) is the number of odd composite numbers up to 2*n-1. - _Michel Marcus_, Aug 05 2023
%H Vincenzo Librandi, <a href="/A210469/b210469.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = n - primepi(2n).
%e a(6) = 1 since 9 is the only odd composite number appearing in the partitions of 2*6 = 12 into two parts. For example, 12 = (1+11) = (2+10) = (3+9) = (4+8) = (5+7) = (6+6). Note that the numbers in the partitions with identical parts are counted only once.
%p with(numtheory); a:=n->n-pi(2*n); seq(a(k), k=1..70);
%t Table[n - PrimePi[2 n], {n, 70}] (* _Robert G. Wilson v_, Jan 24 2013 *)
%o (PARI) a(n) = n - primepi(2*n); \\ _Michel Marcus_, Aug 05 2023
%Y Cf. A099802.
%Y See A224710 for a closely related sequence.
%K nonn,easy
%O 1,8
%A _Wesley Ivan Hurt_, Jan 24 2013
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