A255962 Number of repeating products of any subset of {1, 2, 3, ..., n}.

0, 1, 3, 7, 15, 37, 75, 167, 359, 785, 1571, 3447, 6895, 14367, 29783, 61303, 122607, 250783, 501567, 1018031, 2053407, 4127231, 8254463, 16610879, 33311679, 66737871, 133719583, 267778623, 535557247, 1072160511, 2144321023, 4291006911, 8584417343, 17171483103, 34348627135, 68706410943

Offset: 1

Author

Derek Orr, Mar 11 2015

Keywords

• nonn

Examples

			a(3) = (number of possible subsets of {1,2,3}) - |{1, 2, 3, 1*2, 1*3, 2*3, 1*2*3}| = 2^3-1 - |{1,2,3,6}| = 3. Equivalently, there are three repeating products (2, 3, and 6) so a(3) = 3.
		

Crossrefs

Cf. A000225, A060957.

Programs

Mathematica

(* Script not convenient for n > 24 *) f[n_] := Block[{lst = Times @@@ Subsets[Range@ n, n]}, 2^n - 1 - Length@ Select[Tally@ lst, Last@ # > 1 &]]; Array[f, 16] (* Michael De Vlieger, Mar 13 2015 *)

Formula

a(n) = 2^n - 1 - A060957(n) = A000225(n) - A060957(n).