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

Offset: 1

Author

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

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A000252, A069177.

Programs

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 *)

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

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

Extensions

More terms from Vladeta Jovovic, Apr 17 2002