A054703 Number of distinct powers of 2 modulo n.

1, 2, 2, 3, 4, 3, 3, 4, 6, 5, 10, 4, 12, 4, 4, 5, 8, 7, 18, 6, 6, 11, 11, 5, 20, 13, 18, 5, 28, 5, 5, 6, 10, 9, 12, 8, 36, 19, 12, 7, 20, 7, 14, 12, 12, 12, 23, 6, 21, 21, 8, 14, 52, 19, 20, 6, 18, 29, 58, 6, 60, 6, 6, 7, 12, 11, 66, 10, 22, 13, 35, 9, 9, 37, 20, 20, 30, 13, 39, 8, 54

Offset: 1

Author

Henry Bottomley, Apr 20 2000

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A007733, A007814.

Cf. A054704 (base 3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).

Programs

Mathematica

a[n_] := Module[{e = IntegerExponent[n, 2]}, e + MultiplicativeOrder[2, n/2^e]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

Formula

a(n) = A007814(n) + A007733(n). - Max Alekseyev, May 13 2016

Extensions

Definition improved by T. D. Noe, Jul 21 2008