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%I #9 Feb 24 2024 00:49:13
%S 0,1,1,2,2,3,3,6,6,11,10,18,20,30,35,49,55,77,92,120,145,184,221,283,
%T 340,423,511,627,755,928,1112,1348,1611,1942,2314,2787,3303,3948,4673,
%U 5564,6562,7794,9158,10821,12689,14946,17484,20540,23949,28036,32631
%N Number of partitions of n such that the numbers of prime and composite parts differ by at least 1.
%C a(n) = A002865(n) - A116449(n).
%e n=9: there are 8 partitions of 9 with parts > 1: 9, 7+2, 6+3,
%e 5+4, 5+2+2, 4+3+2, 3+3+3 and 3+2+2+2; two of them have an equal number
%e of prime and composite parts: 3+2*3 and 5+2*2, therefore A116449(9)=2
%e and a(9)=8-2=6.
%K nonn
%O 1,4
%A _Reinhard Zumkeller_, Feb 16 2006
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