OFFSET
2,4
COMMENTS
P. Freyd (see link) writes: A050318 is "the number of isomorphism types of [equationally linear Heyting semi-lattices] of order n ..., albeit shifted by 1." And: "A050318 shifted by 1 is the number of isomorphism types of distributive lattices in which any element below a coprime is itself a coprime. Which ... is the same as the number of distributive lattices in which any element above a prime is itself a prime." - Peter Luschny, Nov 13 2018
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..10000
Peter Freyd, On the size of Heyting Semi-Lattices and Equationally Linear Heyting Algebras, July 17 2017.
FORMULA
Shifts left under transform T where Ta has Dirichlet g.f. Product_{n>=1}(1/(1-1/n^s)^a(n)).
EXAMPLE
The different ways of writing the numbers 2 through 7 as mterms are:
2 = 2,
3 = 1 + 2,
4 = 1 + (1+2),
5 = 1 + (1+1+2) = 1 + 2*2,
6 = 1 + (1+1+1+2) = 1 + (1+2*2),
7 = 1 + (1+1+1+1+2) = 1 + (1+1+2*2) = 1 + 2*(1+2).
PROG
(PARI) seq(n)={my(v=vector(n, i, i==1)); for(k=2, n, v=dirmul(v, vector(#v, i, my(e=valuation(i, k)); if(i==k^e, binomial(v[k-1] + e - 1, e), 0)))); v} \\ Andrew Howroyd, Nov 17 2018
CROSSREFS
KEYWORD
nonn,eigen,nice,easy
AUTHOR
Christian G. Bower, Sep 15 1999
STATUS
approved