OFFSET
1,6
COMMENTS
A rational number q is a nonempty-subset-average of an integer partition y if there exists a nonempty submultiset of y with average q.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
FORMULA
a(n) = A316398(n) - 1.
EXAMPLE
The a(42) = 7 subset-averages of (4,2,1) are 1, 3/2, 2, 7/3, 5/2, 3, 4.
The a(72) = 7 subset-averages of (2,2,1,1,1) are 1, 5/4, 4/3, 7/5, 3/2, 5/3, 2.
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Union[Mean/@Rest[Subsets[primeMS[n]]]]], {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));
A316314(n) = { my(m=Map(), s, k=0); fordiv(n, d, if((d>1)&&!mapisdefined(m, s = v056239[d]/bigomega(d)), mapput(m, s, s); k++)); (k); }; \\ Antti Karttunen, Sep 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 29 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 23 2018
STATUS
approved