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 A057764 Triangle T(n,k) = number of nonzero elements of multiplicative order k in Galois field GF(2^n) (n >= 1, 1 <= k <= 2^n-1). 3
 1, 1, 0, 2, 1, 0, 0, 0, 0, 0, 6, 1, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 1, 0, 2, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Robert Israel, Table of n, a(n) for n = 1..16369 (rows 1 to 13, flattened) FORMULA From Robert Israel, Jul 21 2016: (Start) T(n,k) = A000010(k) if k is a divisor of 2^n-1, otherwise 0. Sum_{k=1..2^n-1} T(n,k) = 2^n-1 = A000225(n). G.f. as triangle: g(x,y) = Sum_{j>=0} x^A002326(j)*A000010(2j+1)*y^(2j+1)/(1-x^A002326(j)). (End) EXAMPLE Table begins: 1; 1, 0, 2; 1, 0, 0, 0, 0, 0, 6; ... MAPLE f:= proc(n, k) if 2^n-1 mod k = 0 then numtheory:-phi(k) else 0 fi end proc: seq(seq(f(n, k), k=1..2^n-1), n=1..10); # Robert Israel, Jul 21 2016 MATHEMATICA T[n_, k_] := If[Divisible[2^n - 1, k], EulerPhi[k], 0]; Table[T[n, k], {n, 1, 10}, {k, 1, 2^n - 1}] // Flatten (* Jean-François Alcover, Feb 07 2023, after Robert Israel *) PROG (Magma) {* Order(g) : g in GF(2^6) | g ne 0 *}; CROSSREFS Cf. A000010, A000225, A002326, A053287. Sequence in context: A277627 A037857 A037875 * A010108 A033782 A302721 Adjacent sequences: A057761 A057762 A057763 * A057765 A057766 A057767 KEYWORD nonn,easy,nice,tabf AUTHOR N. J. A. Sloane, Nov 01 2000 EXTENSIONS T(6,21) corrected by Robert Israel, Jul 21 2016 STATUS approved

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Last modified August 5 05:45 EDT 2024. Contains 374935 sequences. (Running on oeis4.)