OFFSET
1,4
COMMENTS
Every oterm is at least 1 (implicit) and every 1+oterm is at least 2. Therefore to write 1 as a product of (1+oterms) can only be done as an empty product, which has value 1. Therefore a(1) = 1.
a(n) is also the number of non-isomorphic Gödel algebras of cardinality n. - Diego Valota, Jul 03 2019
REFERENCES
Diego Valota (2019) Spectra of Gödel Algebras. In: Silva A., Staton S., Sutton P., Umbach C. (eds) Language, Logic, and Computation. TbiLLC 2018. Lecture Notes in Computer Science, vol 11456. Springer, Berlin, Heidelberg.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..10000
Pietro Codara, Gabriele Maurina, and Diego Valota, Computing Duals of Finite Gödel Algebras, Proceedings of the Federated Conference on Computer Science and Information Systems, Annals of Computer Science and Information Science (2020) Vol. 21, 31-34.
Sean A. Irvine, Java program (github)
Luc Rousseau, A Prolog program that computes A130841.
Luc Rousseau, Illustration that a(12)=12.
FORMULA
a(n) = sum over sequences (n_1,n_2,...,n_k) such that 2 <= n_1 <= n_2 <= ... <= n_k and n1*n2*...*nk=n of Product{j=1..k} a(n_j-1).
EXAMPLE
a(8)=5 because we can write 8 as one of (1+1+1+1+1+1+1+1), (1+1+1+1+(1+1)*(1+1)), (1+1+(1+1)*(1+1+1)), (1+1)*(1+1+1+1), (1+1)*(1+1)*(1+1). [Corrected by Diego Valota, Jul 03 2019]
PROG
(Prolog) % See Rousseau link.
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel R. L. Brown, Jul 19 2007, revised Nov 23 2007
STATUS
approved
