A054705 - OEIS

A054705

Number of powers of 4 modulo n.

1, 2, 1, 2, 2, 2, 3, 3, 3, 3, 5, 2, 6, 4, 2, 3, 4, 4, 9, 3, 3, 6, 11, 3, 10, 7, 9, 4, 14, 3, 5, 4, 5, 5, 6, 4, 18, 10, 6, 4, 10, 4, 7, 6, 6, 12, 23, 3, 21, 11, 4, 7, 26, 10, 10, 5, 9, 15, 29, 3, 30, 6, 3, 4, 6, 6, 33, 5, 11, 7, 35, 5, 9, 19, 10, 10, 15, 7, 39, 4, 27, 11, 41, 4, 4, 8, 14, 7, 11

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OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from David W. Wilson)

FORMULA

a(n) = A007735(n) + A244415(n). - Amiram Eldar, Aug 25 2024

MATHEMATICA

a[n_] := IntegerExponent[2*n, 4] + MultiplicativeOrder[4, n/2^IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

CROSSREFS

Cf. A007735, A244415.