login
A138618
Triangle of exponentials of Mangoldt function M(n) read by rows, in which row products give the natural numbers.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
Mats Granvik, May 14 2008
STATUS
approved