|
%I #9 Oct 05 2018 11:10:04
%S 0,1,1,1,1,2,1,1,1,3,1,2,1,2,2,1,1,2,1,3,3,3,1,2,1,2,1,3,1,3,1,1,2,3,
%T 2,2,1,2,3,3,1,4,1,3,2,3,1,2,1,3,2,2,1,2,3,3,3,2,1,3,1,3,3,1,2,4,1,4,
%U 2,4,1,2,1,2,2,2,2,5,1,3,1,3,1,4,3,2,3,4,1,3,3,3,2,3,2,2,1,3,3,3,1,4,1,2,3
%N Number of distinct integer averages of subsets of the integer partition with Heinz number n.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H Antti Karttunen, <a href="/A316557/b316557.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) <= A316314(n). - _Antti Karttunen_, Sep 25 2018
%e The a(78) = 5 distinct integer averages of subsets of (6,2,1) are {1, 2, 3, 4, 6}.
%t Table[Length[Select[Union[Mean/@Subsets[If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]]],IntegerQ]],{n,100}]
%o (PARI)
%o up_to = 65537;
%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
%o v056239 = vector(up_to,n,A056239(n));
%o A316557(n) = { my(m=Map(),s,k=0); fordiv(n,d,if((d>1)&&(1==denominator(s = v056239[d]/bigomega(d)))&&!mapisdefined(m,s), mapput(m,s,s); k++)); (k); }; \\ _Antti Karttunen_, Sep 25 2018
%Y Cf. A056239, A067538, A122768, A237984, A296150, A316313, A316314, A316440, A316555, A316556.
%K nonn
%O 1,6
%A _Gus Wiseman_, Jul 06 2018
%E More terms from _Antti Karttunen_, Sep 25 2018
|
