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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 (list; graph; refs; listen; history; text; internal format)
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 * A032436 A280274 A073408

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

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Last modified June 22 11:59 EDT 2021. Contains 345375 sequences. (Running on oeis4.)