A047917 Triangular array read by rows: a(n,k) = phi(n/k)*(n/k)^k*k!/n if k|n else 0 (1<=k<=n).

1, 1, 1, 2, 0, 2, 2, 2, 0, 6, 4, 0, 0, 0, 24, 2, 6, 8, 0, 0, 120, 6, 0, 0, 0, 0, 0, 720, 4, 8, 0, 48, 0, 0, 0, 5040, 6, 0, 36, 0, 0, 0, 0, 0, 40320, 4, 20, 0, 0, 384, 0, 0, 0, 0, 362880, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800, 4, 12, 64, 324, 0, 3840, 0, 0, 0, 0

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• nice
• easy

Examples

			1; 1,1; 2,0,2; 2,2,0,6; 4,0,0,0,24; 2,6,8,0,0,120; ...
		

References

• J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
• C. L. Mallows and N. J. A. Sloane, Notes on A002618, A002619, etc.
• N. J. A. Sloane, Notes on A002618, A002619, etc.
• J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.
• J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61. [Annotated scanned copy. Note that the scanned pages are out of order]

Crossrefs

Divide n-th row of A047916 by n.

Row sums give A061417.

Cf. A002024.

Programs

Haskell

a047917 n k = a047917_tabl !! (n-1) !! (k-1)
a047917_row n = a047917_tabl !! (n-1)
a047917_tabl = zipWith (zipWith div) a047916_tabl a002024_tabl
-- Reinhard Zumkeller, Mar 19 2014

Mathematica

a[n_, k_] := If[ Divisible[n, k], EulerPhi[n/k]*(n/k)^k*k!/n, 0]; Flatten[ Table[ a[n, k], {n, 1, 12}, {k, 1, n}]](* Jean-François Alcover, Feb 17 2012 *)

Extensions

Offset corrected by Reinhard Zumkeller, Mar 19 2014