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 A301957 Number of distinct subset-products of the integer partition with Heinz number n. 14
 1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 4, 1, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 4, 2, 2, 4, 2, 1, 4, 2, 4, 3, 2, 2, 4, 2, 2, 4, 2, 2, 6, 2, 2, 2, 3, 3, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 2, 5, 1, 4, 4, 2, 2, 4, 4, 2, 3, 2, 2, 6, 2, 4, 4, 2, 2, 5, 2, 2, 4, 4, 2, 4, 2, 2, 6, 4, 2, 4, 2, 4, 2, 2, 3, 6, 3, 2, 4, 2, 2, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A subset-product of an integer partition y is a product of some submultiset of y. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Number of distinct values obtained when A003963 is applied to all divisors of n. - Antti Karttunen, Sep 05 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 EXAMPLE The distinct subset-products of (4,2,1,1) are 1, 2, 4, and 8, so a(84) = 4. The distinct subset-products of (6,3,2) are 1, 2, 3, 6, 12, 18, and 36, so a(195) = 7. MATHEMATICA Table[If[n===1, 1, Length[Union[Times@@@Subsets[Join@@Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]], {n, 100}] PROG (PARI) up_to = 65537; A003963(n) = { n=factor(n); n[, 1]=apply(primepi, n[, 1]); factorback(n) }; \\ From A003963 v003963 = vector(up_to, n, A003963(n)); A301957(n) = { my(m=Map(), s, k=0, c); fordiv(n, d, if(!mapisdefined(m, s = v003963[d], &c), mapput(m, s, s); k++)); (k); }; \\ Antti Karttunen, Sep 05 2018 CROSSREFS Cf. A000712, A001055, A001227, A002865, A003963, A108917, A162247, A276024, A292886, A301854, A301855, A301856, A301970, A301979, A304793. Sequence in context: A023588 A175242 A225843 * A318874 A001227 A060764 Adjacent sequences:  A301954 A301955 A301956 * A301958 A301959 A301960 KEYWORD nonn AUTHOR Gus Wiseman, Mar 29 2018 EXTENSIONS More terms from Antti Karttunen, Sep 05 2018 STATUS approved

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Last modified April 19 06:30 EDT 2019. Contains 322237 sequences. (Running on oeis4.)