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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.)