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 A316314 Number of distinct nonempty-subset-averages of the integer partition with Heinz number n. 18
 0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 3, 1, 1, 4, 1, 4, 3, 3, 1, 5, 1, 3, 1, 4, 1, 5, 1, 1, 3, 3, 3, 5, 1, 3, 3, 5, 1, 7, 1, 4, 4, 3, 1, 6, 1, 4, 3, 4, 1, 5, 3, 5, 3, 3, 1, 8, 1, 3, 4, 1, 3, 7, 1, 4, 3, 7, 1, 7, 1, 3, 4, 4, 3, 7, 1, 6, 1, 3, 1, 8, 3, 3, 3, 5, 1, 7, 3, 4, 3, 3, 3, 7, 1, 4, 4, 5, 1, 7, 1, 5, 5 (list; graph; refs; listen; history; text; internal format)
 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 Antti Karttunen, Table of n, a(n) for n = 1..65537 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 Cf. A032302, A056239, A108917, A122768, A275972, A276024, A296150, A299701, A299702, A301899, A301957, A304793, A316313. One less than A316398. Sequence in context: A102396 A344852 A095960 * A183093 A183096 A029356 Adjacent sequences: A316311 A316312 A316313 * A316315 A316316 A316317 KEYWORD nonn AUTHOR Gus Wiseman, Jun 29 2018 EXTENSIONS More terms from Antti Karttunen, Sep 23 2018 STATUS approved

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Last modified January 29 11:27 EST 2023. Contains 359922 sequences. (Running on oeis4.)