A138243 Triangle read by rows: Row products give A027642.

1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Mats Granvik, Mar 08 2008

Keywords

• nonn
• tabl

Comments

Except for the first column, the n-th prime number appears in every A006093(n)-th row, beginning at the A000040(n)-th row, in the n-th column.

Examples

			Row products of the first few rows are:
1 = 1
2*1 = 2
2*3*1 = 6
1*1*1*1 = 1
2*3*5*1*1 = 30
1*1*1*1*1*1 = 1
2*3*1*7*1*1*1 = 42
1*1*1*1*1*1*1*1 = 1
2*3*5*1*1*1*1*1*1 = 30
		

Links

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

Crossrefs

Cf. A006093, A027642.

Programs

Maple

T:= (n, k)-> (p-> `if`(irem(denom(bernoulli(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

Table[With[{p = Prime@ k}, p Boole[Divisible[Denominator@ BernoulliB[n - 1], p]]] /. 0 -> 1, {n, 14}, {k, n}] // Flatten (* Michael De Vlieger, Aug 27 2017 *)

PARI

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

Formula

T(n,k) = A000040(k) if A027642(n) mod A000040(k) = 0, 1 otherwise.

Extensions

Offset corrected by Alois P. Heinz, Aug 27 2017