A316557 Number of distinct integer averages of subsets of the integer partition with Heinz number n.

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

Crossrefs

Cf. A056239, A067538, A122768, A237984, A296150, A316313, A316314, A316440, A316555, A316556.

Sequence in context: A241665 A175307 A324825 * A353381 A032436 A360615

Adjacent sequences: A316554 A316555 A316556 * A316558 A316559 A316560

Keyword

nonn

Author

Gus Wiseman, Jul 06 2018

Extensions

More terms from Antti Karttunen, Sep 25 2018

Status

approved