A350380 Triangle read by rows in which row n lists A014963(d), the exponential of Mangoldt function, for each divisor d of n.

1, 1, 2, 1, 3, 1, 2, 2, 1, 5, 1, 2, 3, 1, 1, 7, 1, 2, 2, 2, 1, 3, 3, 1, 2, 5, 1, 1, 11, 1, 2, 3, 2, 1, 1, 1, 13, 1, 2, 7, 1, 1, 3, 5, 1, 1, 2, 2, 2, 2, 1, 17, 1, 2, 3, 1, 3, 1, 1, 19, 1, 2, 2, 5, 1, 1, 1, 3, 7, 1, 1, 2, 11, 1, 1, 23, 1, 2, 3, 2, 1, 2, 1, 1, 1, 5, 5, 1, 2, 13, 1

Offset: 1

Author

Michel Marcus, Dec 28 2021, following a suggestion from Charles Kusniec

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  1;
  1, 2;
  1, 3;
  1, 2, 2;
  1, 5;
  1, 2, 3, 1;
  1, 7;
  1, 2, 2, 2;
  1, 3, 3;
  1, 2, 5, 1;
  ...
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10006 (rows 1 to 1358, flattened).

Crossrefs

Cf. A014963, A027750.

Cf. A000027 (row products), A140255 (row sums).

Programs

Mathematica

Table[Exp[MangoldtLambda[Divisors[n]]], {n, 1, 26}] // Flatten (* Amiram Eldar, Dec 28 2021 *)

PARI

M(n) = ispower(n, , &n); if(isprime(n), n, 1); \\ A014963
row(n) = apply(M, divisors(n));

Formula

a(n) = A014963(A027750(n)).