This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A077564 #13 May 29 2025 02:42:53
%S A077564 1,1,1,2,2,2,3,4,4,5,6,8,10,10,11,14,14,19,22,22,25,30,34,38,40,46,54,
%T A077564 60,63,74,81,85,91,108,118,126,134,153,173,180,186,214,236,245,262,
%U A077564 301,326,338,355,395,437,461,476,540,592,610,649,717,768,811,853,943,1039
%N A077564 Number of partitions of n into parts with distinct prime signatures.
%C A077564 The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.
%H A077564 Sean A. Irvine, <a href="/A077564/b077564.txt">Table of n, a(n) for n = 0..200</a>
%e A077564 a(7) = 4. The partitions are 7, 6+1, 4+3, 4+2+1. (5+2, 3+2+2, ... are not counted.)
%t A077564 sig[n_] := Sort[Last/@FactorInteger[n]]; f[n_, m_] := Module[{sm}, If[n>m(m+1)/2||n<0, Return[{}]]; If[n==0, Return[{{}}]]; sm=sig[m]; f[n, m]=Union[f[n, m-1], Prepend[ #, m]&/@Select[f[n-m, m-1], !MemberQ[sig/@#, sm]&]]]; a[n_] := Length[f[n, n]] (* f[n, m] is list of partitions of n into parts <= m with distinct prime signatures *)
%Y A077564 Cf. A077563.
%K A077564 nonn
%O A077564 0,4
%A A077564 _Amarnath Murthy_, Nov 11 2002
%E A077564 Edited by _Dean Hickerson_, Nov 11 2002