A316556 Number of distinct LCMs of nonempty submultisets of the integer partition with Heinz number n.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 3, 2, 3, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 2, 2, 1, 4, 1, 2, 2, 1, 2, 4, 1, 2, 3, 4, 1, 2, 1, 2, 3, 2, 3, 3, 1, 2, 1, 2, 1, 3, 3, 2, 2, 2, 1, 4, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 4, 1, 2, 5

Offset

1,6

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Number of distinct values obtained when A290103 is applied to all divisors of n larger than one. - Antti Karttunen, Sep 25 2018

Links

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

Example

462 is the Heinz number of (5,4,2,1) which has possible LCMs of nonempty submultisets {1,2,4,5,10,20} so a(462) = 6.

Mathematica

Table[Length[Union[LCM@@@Rest[Subsets[If[n==1, {}, Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]]]]]]], {n, 100}]

Prog

(PARI)
A290103(n) = lcm(apply(p->primepi(p), factor(n)[, 1]));
A316556(n) = { my(m=Map(), s, k=0); fordiv(n, d, if((d>1)&&!mapisdefined(m, s=A290103(d)), mapput(m, s, s); k++)); (k); }; \\ Antti Karttunen, Sep 25 2018

Crossrefs

Cf. A056239, A074761, A108917, A122768, A275972, A290103, A296150, A301957, A316313, A316314, A316430, A316555, A316557.

Cf. also A304793, A305611, A319685, A319695 for other similarly constructed sequences.

Sequence in context: A330746 A316555 A337531 * A187279 A076820 A206824

Adjacent sequences: A316553 A316554 A316555 * A316557 A316558 A316559

Keyword

nonn

Author

Gus Wiseman, Jul 06 2018

Extensions

More terms from Antti Karttunen, Sep 25 2018

Status

approved