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 A054522 Triangle T(n,k): T(n,k) = phi(k) if k divides n, T(n,k)=0 otherwise (n >= 1, 1<=k<=n). T(n,k) = number of elements of order k in cyclic group of order n. 25
 1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 0, 4, 1, 1, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 6, 1, 1, 0, 2, 0, 0, 0, 4, 1, 0, 2, 0, 0, 0, 0, 0, 6, 1, 1, 0, 0, 4, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1, 1, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS T(n,1) = 1; T(n,n) = A000010(n). This triangle is the transpose of the upper triangular array U in the LU decomposition of the square array A003989. - Peter Bala, Oct 15 2023 LINKS Reinhard Zumkeller, Rows n=1..100 of triangle, flattened R. J. Mathar, Plots of cycle graphs of the finite groups up to order 36, (2015) FORMULA Sum (T(n,k): k = 1 .. n) = n. - Reinhard Zumkeller, Oct 18 2011 EXAMPLE 1; 1, 1; 1, 0, 2; 1, 1, 0, 2; 1, 0, 0, 0, 4; 1, 1, 2, 0, 0, 2; 1, 0, 0, 0, 0, 0, 6; 1, 1, 0, 2, 0, 0, 0, 4; 1, 0, 2, 0, 0, 0, 0, 0, 6; MAPLE A054522 := proc(n, k) if modp(n, k) = 0 then numtheory[phi](k) ; else 0; end if; end proc: seq(seq(A054522(n, k), k=1..n), n=1..15) ; # R. J. Mathar, Aug 06 2016 MATHEMATICA t[n_, k_] /; Divisible[n, k] := EulerPhi[k]; t[_, _] = 0; Flatten[Table[t[n, k], {n, 1, 14}, {k, 1, n}]] (* Jean-François Alcover, Nov 25 2011 *) Flatten[Table[If[Divisible[n, k], EulerPhi[k], 0], {n, 15}, {k, n}]] (* Harvey P. Dale, Feb 27 2012 *) PROG (PARI) T(n, k)=if(k<1 || k>n, 0, if(n%k, 0, eulerphi(k))) (Haskell) a054522 n k = a054522_tabl !! (n-1) !! (k-1) a054522_tabl = map a054522_row [1..] a054522_row n = map (\k -> if n `mod` k == 0 then a000010 k else 0) [1..n] -- Reinhard Zumkeller, Oct 18 2011 CROSSREFS Cf. A003989, A054521. Sequence in context: A035183 A178101 A324831 * A110250 A065252 A115211 Adjacent sequences: A054519 A054520 A054521 * A054523 A054524 A054525 KEYWORD nonn,tabl,nice,easy AUTHOR N. J. A. Sloane, Apr 09 2000 STATUS approved

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Last modified April 25 10:01 EDT 2024. Contains 371967 sequences. (Running on oeis4.)