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A138243 Triangle read by rows: Row products give A027642. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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 A246064

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

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Last modified October 15 13:01 EDT 2018. Contains 316236 sequences. (Running on oeis4.)