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A316398 Number of distinct subset-averages of the integer partition with Heinz number n. 2
1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 5, 2, 4, 4, 2, 2, 5, 2, 5, 4, 4, 2, 6, 2, 4, 2, 5, 2, 6, 2, 2, 4, 4, 4, 6, 2, 4, 4, 6, 2, 8, 2, 5, 5, 4, 2, 7, 2, 5, 4, 5, 2, 6, 4, 6, 4, 4, 2, 9, 2, 4, 5, 2, 4, 8, 2, 5, 4, 8, 2, 8, 2, 4, 5, 5, 4, 8, 2, 7, 2, 4, 2, 9, 4, 4, 4, 6, 2, 8, 4, 5, 4, 4, 4, 8, 2, 5, 5, 6, 2, 8, 2, 6, 6 (list; graph; refs; listen; history; text; internal format)
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

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to Heinz numbers

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

Cf. A032302, A056239, A108917, A275972, A276024, A296150, A299701, A301899, A301957, A316313.

One more than A316314.

Sequence in context: A034444 A318465 A073180 * A183095 A304817 A242802

Adjacent sequences:  A316395 A316396 A316397 * A316399 A316400 A316401

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 01 2018

EXTENSIONS

More terms from Antti Karttunen, Sep 23 2018

STATUS

approved

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Last modified April 19 16:46 EDT 2019. Contains 322282 sequences. (Running on oeis4.)