A382508 a(n) is the number of solutions to the problem described in A381621 with smallest price equal to n.

4728, 2314, 1165, 2169, 1429, 703, 304, 1006, 283, 1532, 129, 351, 135, 241, 595, 668, 58, 175, 72, 511, 60, 136, 52, 166, 994, 51, 36, 110, 35, 331, 15, 123, 12, 49, 109, 69, 20, 39, 12, 301, 18, 36, 20, 37, 57, 31, 19, 74, 6, 315, 11, 29, 8, 10, 38, 24, 10, 25, 6, 95

Offset: 1

Author

Hugo Pfoertner, Mar 30 2025

Keywords

• nonn
• fini
• full

Examples

			a(71) = 0 because no 4-tuple with smallest element = 71 exists.
a(91) = 1 because the only 4-tuple with smallest element 91 is [91, 100, 110, 301000].
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..125

Crossrefs

Cf. A381619, A381620, A381621.

Programs

Mathematica

(* Uses a tested heuristic upper bound for the second element b in the 4-tuple; running times > 10 minutes for small n, depending on the computer speed *)
a382508[n_] := Sum[Length[Solve[10^6*(n+b+c+d) == n*b*c*d && c>=b && d>=c,{c,d}, Integers]], {b, n, 111+Floor[1600/n^0.55-n/2]}];