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A382510 a(n) is the number of solutions to the "sum equals product" riddle with n prices v_j, i.e., find positive integers v_j, v_{j+1}>=v_j such that 100^(n-1)*Sum_{k=1..n} v_k = Product_{k=1..n} v_k.

%I A382510 #6 Apr 01 2025 21:37:34
%S A382510 1,13,622,22640
%N A382510 a(n) is the number of solutions to the "sum equals product" riddle with n prices v_j, i.e., find positive integers v_j, v_{j+1}>=v_j such that 100^(n-1)*Sum_{k=1..n} v_k = Product_{k=1..n} v_k.
%C A382510 See A380887 and A381619 for more information.
%e A382510 a(1) = 1: [100] is the only solution.
%e A382510 a(2) = 13: the 13 solutions are [101, 10100], [102, 5100], [104, 2600], [105, 2100], [108, 1350], [110, 1100], [116, 725], [120, 600], [125, 500], [140, 350], [150, 300], [180, 225], [200, 200].
%e A382510 a(3) = 622 is the number of terms of A381619.
%e A382510 a(4) = 22640 is the number of terms of A381621.
%t A382510 Length[Solve[100*(a + b) == a*b && a > 0 && b >= a, {a, b}, Integers]] (* Computes a(2) *)
%Y A382510 Cf. A380887, A381619, A381620, A381621, A382508.
%K A382510 nonn,bref,hard,more
%O A382510 1,2
%A A382510 _Hugo Pfoertner_, Apr 01 2025