A164306 Triangle read by rows: T(n, k) = k / gcd(k, n), 1 <= k <= n.

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 4, 1, 1, 1, 1, 2, 5, 1, 1, 2, 3, 4, 5, 6, 1, 1, 1, 3, 1, 5, 3, 7, 1, 1, 2, 1, 4, 5, 2, 7, 8, 1, 1, 1, 3, 2, 1, 3, 7, 4, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 5, 1, 7, 2, 3, 5, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1

Offset: 1

Author

Reinhard Zumkeller, Aug 12 2009

Keywords

• nonn
• tabl

Comments

Also the gcd of the coefficients of the partition polynomials (called 'De Moivre polynomials' by O'Sullivan, see link, Theorem 4.1). - Peter Luschny, Sep 20 2022

Examples

			From _Indranil Ghosh_, Feb 14 2017: (Start)
Triangle begins:
1,
1, 1,
1, 2, 1,
1, 1, 3, 1,
1, 2, 3, 4, 1,
1, 1, 1, 2, 5, 1,
1, 2, 3, 4, 5, 6, 1,
. . .
T(4,3) = 3 / gcd(3,4) = 3 / 1 = 3. (End)
		

Links

• Indranil Ghosh, Rows 1..120 of triangle, flattened.
• Cormac O'Sullivan, De Moivre and Bell polynomials, arXiv:2203.02868 [math.CO], 2022.

Crossrefs

Cf. A051537, A054531, A057661, A167192.

Programs

Maple

seq(seq(k / igcd(n, k), k = 1..n), n = 1..13); # Peter Luschny, Sep 20 2022

Mathematica

Flatten[Table[k/GCD[k,n],{n,20},{k,n}]] (* Harvey P. Dale, Jul 21 2013 *)

PARI

for(n=0,10, for(k=1,n, print1(k/gcd(k,n), ", "))) \\ G. C. Greubel, Sep 13 2017

Formula

Sum of n-th row = A057661(n).

T(n, k) = A051537(n, k)/A054531(n, k). - Reinhard Zumkeller, Oct 30 2009