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A069256
Size of the Sylow 2-subgroup of the group GL_2(Z_n): maximal power of 2 that divides A000252(n).
1
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
1,2
LINKS
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
Sequence in context: A321308 A109210 A056707 * A344016 A279034 A120069
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