A069256 - OEIS

A069256

Size of the Sylow 2-subgroup of the group GL_2(Z_n): maximal power of 2 that divides A000252(n).

1, 2, 16, 32, 32, 32, 32, 512, 16, 64, 16, 512, 32, 64, 512, 8192, 512, 32, 16, 1024, 512, 32, 32, 8192, 32, 64, 16, 1024, 32, 1024, 128, 131072, 256, 1024, 1024, 512, 32, 32, 512, 16384, 128, 1024, 16, 512, 512, 64, 64, 131072, 32, 64, 8192, 1024, 32, 32, 512

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(2^e) = 2^(4*e-3) and a(p^e) = power of 2 in prime factorization of (p - 1)*(p^2-1) for an odd prime p. - Vladeta Jovovic, Apr 17 2002

MATHEMATICA

f[p_, e_] := 2^IntegerExponent[(p-1)*(p^2-1), 2]; f[2, e_] := 2^(4*e-3); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 02 2023 *)

PROG

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 1] == 2, 1 << (4*f[i, 2]-3), 1 << valuation((f[i, 1]-1)*(f[i, 1]^2-1), 2))); } \\ Amiram Eldar, Nov 03 2023

CROSSREFS

Cf. A000252, A069177.

Sequence in context: A321308 A109210 A056707 * A344016 A279034 A120069

Adjacent sequences: A069253 A069254 A069255 * A069257 A069258 A069259

KEYWORD

nonn,easy,mult

AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), Apr 14 2002

EXTENSIONS

More terms from Vladeta Jovovic, Apr 17 2002

STATUS

approved