A238446 Let B be a nonempty and proper subset of A_n = {1,2,...,p_n-1}, where p_n is the n-th prime. Let C be the complement of B, so that the union B and C is A_n. a(n) is half the number of sums of products of elements of B and elements of C which are divisible by p_n, when B runs through all such subsets of A_n.

0, 1, 3, 11, 103, 343, 4095, 14571, 190651, 9586983, 35791471, 1908874583, 27487790719, 104715393911, 1529755308211, 86607685141743, 4969489243995031, 19215358410149343, 1117984489315857511, 16865594581677305359, 65588423373189982911

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Feb 26 2014

Keywords

• nonn

Examples

			Take A_3 ={1,2,3,4}.  The nonempty and proper subsets are: {{1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}}.
Sums of products of elements of B and elements of C are: 1+2*3*4=25, and analogously 14,11,10,14,11,10,10,11,14,10,11,14,25.
We have 6 numbers divisible by 5. So a(3)=6/2=3.
		

Crossrefs

Cf. A238444, A038791.

Formula

a(n) = A038791(n) - 1. - Ridouane Oudra, Jul 08 2025

Extensions

Name edited and more terms from Ridouane Oudra, Jul 08 2025