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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.

%I A238446 #20 Jul 13 2025 17:41:39
%S A238446 0,1,3,11,103,343,4095,14571,190651,9586983,35791471,1908874583,
%T A238446 27487790719,104715393911,1529755308211,86607685141743,
%U A238446 4969489243995031,19215358410149343,1117984489315857511,16865594581677305359,65588423373189982911
%N 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.
%F A238446 a(n) = A038791(n) - 1. - _Ridouane Oudra_, Jul 08 2025
%e A238446 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}}.
%e A238446 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.
%e A238446 We have 6 numbers divisible by 5. So a(3)=6/2=3.
%Y A238446 Cf. A238444, A038791.
%K A238446 nonn
%O A238446 1,3
%A A238446 _Vladimir Shevelev_ and _Peter J. C. Moses_, Feb 26 2014
%E A238446 Name edited and more terms from _Ridouane Oudra_, Jul 08 2025