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 A077563 #13 May 28 2025 23:10:00 %S A077563 0,0,0,1,1,1,2,2,2,3,3,5,4,4,5,6,4,8,6,8,6,8,8,11,7,10,10,12,10,12,10, %T A077563 13,10,15,12,15,10,17,16,17,13,18,16,18,16,19,18,21,13,20,19,25,20,23, %U A077563 19,24,20,25,24,27,19,24,26,28,21,28,25,30,26,31,26,32,19,30,30,33,30 %N A077563 Number of partitions into two parts which have different prime signatures. %C A077563 The 'prime signature' of n is the sorted list of exponents in the prime factorization of n. %C A077563 Does lim n->infinity a(n)/n exist? If not, what are the limsup and liminf of a(n)/n? %H A077563 Sean A. Irvine, <a href="/A077563/b077563.txt">Table of n, a(n) for n = 0..10000</a> %e A077563 a(9) = 3; the partitions are 8+1, 6+3 and 5+4. %t A077563 sig[n_] := Sort[Last/@FactorInteger[n]]; a[n_] := Length[Select[Range[Floor[n/2]], sig[ # ]!=sig[n-# ]&]] %Y A077563 Cf. A077564. %K A077563 nonn %O A077563 0,7 %A A077563 _Amarnath Murthy_, Nov 11 2002 %E A077563 Edited by _Dean Hickerson_, Nov 11 2002