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A321647 Number of distinct row/column permutations of the Ferrers diagram of the integer partition with Heinz number n.

%I A321647 #10 Feb 09 2019 23:26:26
%S A321647 1,1,1,1,1,4,1,1,1,6,1,6,1,8,6,1,1,6,1,9,12,10,1,8,1,12,1,12,1,36,1,1,
%T A321647 20,14,8,12,1,16,30,12,1,72,1,15,9,18,1,10,1,9,42,18,1,8,20,16,56,20,
%U A321647 1,72,1,22,18,1,40,120,1,21,72,72,1,20,1,24,9,24,10,180,1,15,1,26,1,144,70,28,90,20,1,72,30,27,110,30,112,12,1,12
%N A321647 Number of distinct row/column permutations of the Ferrers diagram of the integer partition with Heinz number n.
%C A321647 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321647 Antti Karttunen, <a href="/A321647/b321647.txt">Table of n, a(n) for n = 1..16384</a>
%F A321647 a(n) = A008480(n) * A008480(A122111(n)) = A008480(n) * A321648(n).
%e A321647 The a(10) = 6 permutations:
%e A321647   o o   o o   o     o       o     o
%e A321647   o       o   o o   o     o o     o
%e A321647   o       o   o     o o     o   o o
%e A321647 The a(21) = 12 permutations:
%e A321647   o o   o o   o o   o o   o o   o o   o     o     o       o     o     o
%e A321647   o o   o o   o     o       o     o   o o   o o   o     o o   o o     o
%e A321647   o       o   o o   o     o o     o   o o   o     o o   o o     o   o o
%e A321647   o       o   o     o o     o   o o   o     o o   o o     o   o o   o o
%t A321647 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A321647 conj[y_]:=If[Length[y]==0,y,Table[Length[Select[y,#>=k&]],{k,1,Max[y]}]];
%t A321647 Table[Length[Permutations[primeMS[n]]]*Length[Permutations[conj[primeMS[n]]]],{n,50}]
%o A321647 (PARI)
%o A321647 A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ From A008480
%o A321647 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 A321647 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A321647 A321647(n) = (A008480(n) * A008480(A122111(n))); \\ _Antti Karttunen_, Feb 09 2019
%Y A321647 Cf. A000219, A008480, A049311, A056239, A068313, A101370, A112798, A122111, A296150, A321645, A321646, A321648, A321655.
%K A321647 nonn
%O A321647 1,6
%A A321647 _Gus Wiseman_, Nov 15 2018
%E A321647 More terms from _Antti Karttunen_, Feb 09 2019