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

0,2

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.

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A006093, A027642.

Sequence in context: A094646 A124448 A143343 * A273136 A273137 A362947

Adjacent sequences: A138240 A138241 A138242 * A138244 A138245 A138246

Keyword

nonn,tabl

Author

Mats Granvik, Mar 08 2008

Extensions

Offset corrected by Alois P. Heinz, Aug 27 2017

Status

approved