A296992 Largest number m such that n^m divides tau(n), where tau(n) = A000594(n) is Ramanujan's tau function.

3, 2, 3, 1, 3, 1, 3, 2, 1, 0, 2, 0, 1, 1, 3, 0, 2, 0, 1, 2, 0, 0, 3, 1, 0, 2, 1, 0, 1, 0, 3, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0

Offset

2,1

Links

Amiram Eldar, Table of n, a(n) for n = 2..10000

Eric Weisstein's World of Mathematics, Tau Function.

Example

tau(2) =   -24 and 2^3 divides   24, so a(2) = 3.
tau(3) =   252 and 3^2 divides  252, so a(3) = 2.
tau(4) = -1472 and 4^3 divides 1472, so a(4) = 3.

Mathematica

f[n_] := Block[{m = 0}, While[Mod[RamanujanTau@n, n^m] == 0, m++]; m - 1]; Array[f, 93, 2] (* Robert G. Wilson v, Dec 23 2017 *)
a[n_] := IntegerExponent[RamanujanTau[n], n]; Array[a, 100, 2] (* Amiram Eldar, Jan 09 2025 *)

Prog

(PARI) a(n) = valuation(ramanujantau(n), n); \\ Amiram Eldar, Jan 09 2025

Crossrefs

Cf. A063938 (a(n)>=1), A296991 (a(n)>=2), A296993 (a(n)>=3).

Cf. A191599 (a(n)=0), A297000 (a(n)=1), A297001 (a(n)=2).

Sequence in context: A082391 A283977 A248579 * A304783 A316830 A345440

Adjacent sequences: A296989 A296990 A296991 * A296993 A296994 A296995

Keyword

nonn

Author

Seiichi Manyama, Dec 22 2017

Status

approved