cp's OEIS Frontend

A112020 Number of partitions of n into distinct semiprimes.

%I A112020 #22 Mar 19 2024 09:13:32
%S A112020 1,0,0,0,1,0,1,0,0,1,2,0,0,1,2,2,1,0,1,3,2,2,1,2,3,5,2,2,3,5,4,5,3,4,
%T A112020 6,9,6,5,6,10,10,9,7,9,12,14,12,11,14,18,17,16,16,19,21,24,21,23,26,
%U A112020 29,30,32,31,33,39,40,39,41,45,49,54,53,54,59,68,66,68,70,78,82,88,86,93,101
%N A112020 Number of partitions of n into distinct semiprimes.
%H A112020 Alois P. Heinz, <a href="/A112020/b112020.txt">Table of n, a(n) for n = 0..10000</a>
%e A112020 For n=4 one partition: {2*2}.
%e A112020 For n=6 one partition: {2*3}.
%e A112020 For n=10 two partitions: {2*2+2*3,2*5}.
%p A112020 h:= proc(n) option remember; `if`(n=0, 0,
%p A112020      `if`(numtheory[bigomega](n)=2, n, h(n-1)))
%p A112020     end:
%p A112020 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A112020       b(n-i, h(min(n-i, i-1)))+b(n, h(i-1))))
%p A112020     end:
%p A112020 a:= n-> b(n, h(n)):
%p A112020 seq(a(n), n=0..100);  # _Alois P. Heinz_, Mar 19 2024
%t A112020 nmax = 100;
%t A112020 CoefficientList[Series[Product[1+x^(Prime[j] Prime[k]), {j, 1, nmax}, {k, j, nmax}], {x, 0, nmax}], x] (* _Jean-François Alcover_, Nov 10 2021 *)
%Y A112020 Cf. A101048, A112022, A001358, A000586.
%K A112020 nonn
%O A112020 0,11
%A A112020 _Reinhard Zumkeller_, Aug 26 2005