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A321648 Number of permutations of the conjugate of the integer partition with Heinz number n.

%I A321648 #11 Dec 30 2018 00:03:56
%S A321648 1,1,1,1,1,2,1,1,1,3,1,2,1,4,3,1,1,2,1,3,6,5,1,2,1,6,1,4,1,6,1,1,10,7,
%T A321648 4,2,1,8,15,3,1,12,1,5,3,9,1,2,1,3,21,6,1,2,10,4,28,10,1,6,1,11,6,1,
%U A321648 20,20,1,7,36,12,1,2,1,12,3,8,5,30,1,3,1,13
%N A321648 Number of permutations of the conjugate of the integer partition with Heinz number n.
%C A321648 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321648 Antti Karttunen, <a href="/A321648/b321648.txt">Table of n, a(n) for n = 1..16384</a>
%F A321648 a(n) = A008480(A122111(n)).
%e A321648 The a(42) = 12 permutations: (3211), (3121), (3112), (2311), (2131), (2113), (1321), (1312), (1231), (1213), (1132), (1123).
%t A321648 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A321648 conj[y_]:=If[Length[y]==0,y,Table[Length[Select[y,#>=k&]],{k,1,Max[y]}]];
%t A321648 Table[Length[Permutations[conj[primeMS[n]]]],{n,50}]
%o A321648 (PARI)
%o A321648 A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ From A008480
%o A321648 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A321648 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A321648 A321648(n) = A008480(A122111(n)); \\ _Antti Karttunen_, Dec 23 2018
%Y A321648 Cf. A008480, A056239, A112798, A122111, A296150, A321645, A321646, A321647, A321649, A321650.
%K A321648 nonn
%O A321648 1,6
%A A321648 _Gus Wiseman_, Nov 15 2018