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 A085288 #21 Feb 16 2025 08:32:50 %S A085288 1,1,3,3,10,10,30,75,220,220,588,588,1568,3696,11616,11616,30492, %T A085288 30492,84700,173250,441000,441000,1262520,2777544,6957720,16731660, %U A085288 43506760,43506760,98658000,98658000,277101000,541886400,1322481600,2715495552 %N A085288 Number of sorted multiplicative partitions of n!. %C A085288 Number of decompositions of n! into factors of the form (p_k)^(e^k). %H A085288 Amiram Eldar, <a href="/A085288/b085288.txt">Table of n, a(n) for n = 2..6940</a> %H A085288 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Alladi-GrinsteadConstant.html">Alladi-Grinstead Constant</a> %F A085288 a(n) = A000688(n!) = A000688(A000142(n)). - _Vladeta Jovovic_, Jun 27 2003 %e A085288 4! = 3*8 = 2*3*4 = 2*2*2*3, so a(4)=3. %e A085288 5! = 3*5*8 = 2*3*4*5 = 2*2*2*3*5, so a(5)=3. %t A085288 f[n_] := Times @@ PartitionsP /@ Last /@ FactorInteger[ n!]; Array[f, 34, 2] (* _Robert G. Wilson v_, Sep 22 2006 *) %Y A085288 Cf. A000142, A000688, A085289, A085290, A085291. %K A085288 nonn %O A085288 2,3 %A A085288 _Eric W. Weisstein_, Jun 23 2003 %E A085288 More terms from _Vladeta Jovovic_, Jun 27 2003