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A301957
Number of distinct subset-products of the integer partition with Heinz number n.
19
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
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 05 2018
STATUS
approved