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.

1, 13, 622, 22640

Offset: 1

Author

Hugo Pfoertner, Apr 01 2025

Keywords

• nonn
• bref
• hard
• more

Comments

See A380887 and A381619 for more information.

Examples

			a(1) = 1: [100] is the only solution.
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].
a(3) = 622 is the number of terms of A381619.
a(4) = 22640 is the number of terms of A381621.
		

Crossrefs

Cf. A380887, A381619, A381620, A381621, A382508.

Programs

Mathematica

Length[Solve[100*(a + b) == a*b && a > 0 && b >= a, {a, b}, Integers]] (* Computes a(2) *)