A138239 Triangle read by rows: T(n,k) = A000040(k) if A002445(n) mod A000040(k) = 0, otherwise 1.

1, 2, 3, 2, 3, 5, 2, 3, 1, 7, 2, 3, 5, 1, 1, 2, 3, 1, 1, 11, 1, 2, 3, 5, 7, 1, 13, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 17, 1, 1, 2, 3, 1, 7, 1, 1, 1, 19, 1, 1, 2, 3, 5, 1, 11, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 2, 3, 5, 7, 1, 13, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Mats Granvik, Mar 07 2008

Keywords

• nonn
• tabl

Comments

Row products give A002445.

A prime number appears in a column at every A130290-th row from the (A130290+1)-th row onwards. The prime numbers are, so to speak, equidistantly distributed in the columns. A130290 is essentially A005097. Counting terms > 1 in the rows gives A046886.

Examples

			First few rows of the triangle and row products are:
1 = 1
2*3 = 6
2*3*5 = 30
2*3*1*7 = 42
2*3*5*1*1 = 30
2*3*1*1*11*1 = 66
2*3*5*7*1*13*1 = 2730
		

Links

• Michel Marcus, Rows n=0..100 of triangle, flattened

Crossrefs

Cf. A002445, A005097, A046886, A130290.

Programs

Maple

T:= (n, k)-> (p-> `if`(irem(denom(bernoulli(2*n)), p)=0, p, 1))(ithprime(k)):
seq(seq(T(n, k), k=1..n+1), n=0..20);  # Alois P. Heinz, Aug 27 2017

Mathematica

t[n_, k_] := If[Mod[Denominator[BernoulliB[2n]], (p = Prime[k])] == 0, p, 1];
Flatten[Table[t[n, k], {n, 0, 13}, {k, 1, n+1}]][[1 ;; 102]] (* Jean-François Alcover, Jun 16 2011 *)

PARI

tabl(nn) = {for (n=0, nn, dbn = denominator(bernfrac(2*n)); for (k=1, n+1, if (! (dbn % prime(k)), w = prime(k), w = 1); print1(w, ", "); ); print; ); } \\ Michel Marcus, Aug 27 2017

Extensions

Definition edited by N. J. A. Sloane, Mar 18 2010

Offset corrected by Alois P. Heinz, Aug 27 2017