cp's OEIS Frontend

A319567 Product of y divided by the GCD of y to the power of the length of y, where y is the integer partition with Heinz number n.

%I A319567 #11 Nov 09 2018 21:44:09
%S A319567 1,1,1,1,1,2,1,1,1,3,1,2,1,4,6,1,1,4,1,3,2,5,1,2,1,6,1,4,1,6,1,1,10,7,
%T A319567 12,4,1,8,3,3,1,8,1,5,12,9,1,2,1,9,14,6,1,8,15,4,4,10,1,6,1,11,2,1,2,
%U A319567 10,1,7,18,12,1,4,1,12,18,8,20,12,1,3,1,13
%N A319567 Product of y divided by the GCD of y to the power of the length of y, where y is the integer partition with Heinz number n.
%C A319567 The Heinz number of a partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%F A319567 a(n) = A003963(n) / A289508(n) ^ A001222(n).
%t A319567 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A319567 Table[If[n==1,1,Times@@primeMS[n]/GCD@@primeMS[n]^PrimeOmega[n]],{n,100}]
%Y A319567 Cf. A003963, A001222, A056239, A067538, A112798, A143773, A289508, A289509, A316430.
%K A319567 nonn
%O A319567 0,6
%A A319567 _Gus Wiseman_, Sep 23 2018