A138618 Triangle of exponentials of Mangoldt function M(n) read by rows, in which row products give the natural numbers.

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

Offset

1,2

Comments

Row sums are A001414. This table is similar to A139547 and A120885.

Cumulative column products are A003418, A139550, A139552, A139554.

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Mangoldt Function.

Formula

T(n,k) = A014963(n/k) if n mod k = 0, otherwise 1. - Mats Granvik, May 23 2013

Example

1 = 1
2*1 = 2
3*1*1 = 3
2*2*1*1 = 4
5*1*1*1*1 = 5
1*3*2*1*1*1 = 6
7*1*1*1*1*1*1 = 7
2*2*1*2*1*1*1*1 = 8
3*1*3*1*1*1*1*1*1 = 9
1*5*1*1*2*1*1*1*1*1 = 10
11*1*1*1*1*1*1*1*1*1*1 = 11
1*1*2*3*1*2*1*1*1*1*1*1 = 12
13*1*1*1*1*1*1*1*1*1*1*1*1 = 13

Mathematica

Flatten[Table[Table[If[Mod[n, k] == 0, Exp[MangoldtLambda[n/k]], 1], {k, 1, n}], {n, 1, 14}]] (* Mats Granvik, May 23 2013 *)

Prog

(PARI) M(n) = ispower(n, , &n); if(isprime(n), n, 1); \\ A014963
T(n, k) = if (n % k, 1, M(n/k));
row(n) = vector(n, k, T(n, k)); \\ Michel Marcus, Mar 03 2023

Crossrefs

Cf. A120885, A139547, A001414, A000027.

Sequence in context: A087157 A351094 A351092 * A140583 A237266 A123507

Adjacent sequences: A138615 A138616 A138617 * A138619 A138620 A138621

Keyword

nonn,tabl

Author

Mats Granvik, May 14 2008

Status

approved