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%I #8 Sep 23 2018 21:26:39
%S 1,2,2,2,2,4,2,2,2,4,2,5,2,4,4,2,2,5,2,5,4,4,2,6,2,4,2,5,2,6,2,2,4,4,
%T 4,6,2,4,4,6,2,8,2,5,5,4,2,7,2,5,4,5,2,6,4,6,4,4,2,9,2,4,5,2,4,8,2,5,
%U 4,8,2,8,2,4,5,5,4,8,2,7,2,4,2,9,4,4,4,6,2,8,4,5,4,4,4,8,2,5,5,6,2,8,2,6,6
%N Number of distinct subset-averages of the integer partition with Heinz number n.
%C Although the average of an empty set is technically indeterminate, we consider it to be distinct from the other subset-averages.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H Antti Karttunen, <a href="/A316398/b316398.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>
%F a(n) = A316314(n) + 1.
%e The a(60) = 9 distinct subset-averages of (3,2,1,1) are 0/0, 1, 4/3, 3/2, 5/3, 7/4, 2, 5/2, 3.
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Length[Union[Mean/@Subsets[primeMS[n]]]],{n,100}]
%o (PARI)
%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
%o A316398(n) = { my(m=Map(),s,k=0); fordiv(n,d,if((d>1)&&!mapisdefined(m,s = A056239(d)/bigomega(d)), mapput(m,s,s); k++)); (1+k); }; \\ _Antti Karttunen_, Sep 23 2018
%Y Cf. A032302, A056239, A108917, A275972, A276024, A296150, A299701, A301899, A301957, A316313.
%Y One more than A316314.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 01 2018
%E More terms from _Antti Karttunen_, Sep 23 2018
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