OFFSET
1,2
COMMENTS
Although the average of an empty set is technically indeterminate, we consider it to be distinct from the other subset-averages.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
FORMULA
a(n) = A316314(n) + 1.
EXAMPLE
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.
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Union[Mean/@Subsets[primeMS[n]]]], {n, 100}]
PROG
(PARI)
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 01 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 23 2018
STATUS
approved