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
KEYWORD
AUTHOR
N. J. A. Sloane, Apr 09 2000
STATUS
approved