A266875 Number of partially ordered sets ("posets") with n labeled elements, modulo n.

0, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 4, 3, 1, 9, 1

Offset: 1

Author

Altug Alkan, Jan 05 2016

Keywords

• nonn
• more

Comments

If n is a prime number, a(n) = 1 because of the fact that A001035(p^k) == 1 mod p for all primes p.

If n is an even number, a(n) is a number of the form 3^k for n <= 19. How is the distribution of terms of the form 3^k in this sequence?

Examples

			a(4) = A001035(4) mod 4 = 219 mod 4 = 3.
a(5) = A001035(5) mod 5 = 4231 mod 5 = 1.
a(6) = A001035(6) mod 6 = 130023 mod 6 = 3.
a(7) = A001035(7) mod 7 = 6129859 mod 7 = 1.
		

Crossrefs

Cf. A001035, A265847.

Formula

a(n) = A001035(n) mod n, for n > 0.

a(A000040(n)) = A265847(A000040(n)) - 1, for n > 1.