A301957 Number of distinct subset-products of the integer partition with Heinz number n.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

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: A355770 A225843 A327657 * A318874 A001227 A369466

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