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A316557
Number of distinct integer averages of subsets of the integer partition with Heinz number n.
4
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, 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, 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
OFFSET
1,6
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
FORMULA
a(n) <= A316314(n). - Antti Karttunen, Sep 25 2018
EXAMPLE
The a(78) = 5 distinct integer averages of subsets of (6,2,1) are {1, 2, 3, 4, 6}.
MATHEMATICA
Table[Length[Select[Union[Mean/@Subsets[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]], IntegerQ]], {n, 100}]
PROG
(PARI)
up_to = 65537;
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
v056239 = vector(up_to, n, A056239(n));
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 06 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 25 2018
STATUS
approved