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%I #15 Jan 12 2019 03:27:47
%S 2,5,11,11,22,42,77,77,135,231,385,385,627,1002,627,1575,1575,2436,
%T 3718,5604,5604,8349,5604,12310,17977,17977,26015,37338,53174,53174,
%U 75175,105558,53174,147273,147273,204226,281589,204226,386155,386155
%N Number of partitions of n-th composite number containing the smallest prime factor: a(n) = A027293(A002808(n), A056608(n)).
%C a(n) = A000041(A002808(n)) - A091094(n).
%C a(n) = A000041(A085271(n)). - _Charlie Neder_, Jan 10 2019
%e n=2: A002808(2)=6=2*3 has A000041(6)=11 partitions: 6 = 5+1 = 4+2 = 4+1+1 = 3+3 = 3+2+1 = 3+1+1+1 = 2+2+2 = 2+2+1+1 = 2+1+1+1+1 = 1+1+1+1+1+1, 2 occurs in 5 partitions, therefore a(2)=5.
%o (PARI) lista(nn) = forcomposite(n=2, nn, print1(numbpart(n - divisors(n)[2]), ", ")); \\ _Michel Marcus_, Jan 11 2019
%Y Cf. A002808, A000041, A020639, A027293, A056608, A085271, A091109, A091094.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Feb 22 2004
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