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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
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
Sequence in context: A035183 A178101 A324831 * A110250 A065252 A115211
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.)