cp's OEIS Frontend

A024937 a(n) = number of 2's in all partitions of n into distinct primes.

%I A024937 #16 Sep 07 2022 04:10:16
%S A024937 0,0,1,0,0,1,0,1,0,1,1,0,1,1,1,1,1,1,2,1,2,2,2,2,2,3,3,2,3,3,3,4,3,5,
%T A024937 4,4,5,5,6,6,5,7,7,7,8,8,9,8,9,11,11,10,12,12,13,14,14,16,15,16,17,19,
%U A024937 20,20,20,22,24,23,26,27,27,28,30,33,34,34,36,37,40,41,43,46,46,47,50,55,56,56,58,63,64
%N A024937 a(n) = number of 2's in all partitions of n into distinct primes.
%H A024937 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a024/A024937.java">Java program</a> (github)
%F A024937 G.f.: x^2*Product_{k>1} (1+x^prime(k)). - _Vladeta Jovovic_, Jul 20 2003
%p A024937 with(numtheory):
%p A024937 b:= proc(n, i) option remember; local g;
%p A024937     if n=0 then [1, 0]
%p A024937     elif i<1 then [0, 0]
%p A024937     else g:= `if`(ithprime(i)>n, [0$2], b(n-ithprime(i), i-1));
%p A024937          b(n, i-1) +g +[0, `if`(i=1,g[1],0)]
%p A024937     fi
%p A024937 end:
%p A024937 a:= n-> b(n, pi(n))[2]:
%p A024937 seq(a(n), n=0..80);  # _Sean A. Irvine_, after _Alois P. Heinz_, Jul 29 2019
%t A024937 max = 100; (* number of terms *)
%t A024937 CoefficientList[x^2*Product[1+x^Prime[k], {k, 2, PrimePi[max]}]+O[x]^max, x] (* _Jean-François Alcover_, Sep 07 2022, after _Vladeta Jovovic_ *)
%Y A024937 Cf. A024939.
%K A024937 nonn
%O A024937 0,19
%A A024937 _Clark Kimberling_
%E A024937 More terms from _Vladeta Jovovic_, Jul 20 2003
%E A024937 a(0)-a(6) prepended by _Sean A. Irvine_, Jul 29 2019