A140694 a(n) = A014963(n) * A063659(n).

1, 4, 9, 6, 25, 6, 49, 12, 24, 10, 121, 9, 169, 14, 15, 24, 289, 16, 361, 15, 21, 22, 529, 18, 120, 26, 72, 21, 841, 30, 961, 48, 33, 34, 35, 24, 1369, 38, 39, 30, 1681, 42, 1849, 33, 40, 46, 2209, 36, 336, 48, 51, 39, 2809, 48, 55, 42, 57, 58, 3481, 45, 3721

Offset: 1

Author

Gary W. Adamson and Mats Granvik, May 23 2008

Keywords

• nonn
• easy

Comments

A140579 as an infinite lower triangular matrix * A063659 as a vector.

Examples

			a(4) = A014963(4) * A063659(4) = 2 * 3  = 6.
		

Crossrefs

Cf. A008683, A014963, A063659, A140579.

Programs

Mathematica

f[p_, e_] := If[e == 1, p, p^e - p^(e - 2)]; a[n_] := Exp[MangoldtLambda[n]] * Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 18 2025 *)

Formula

a(n) = n^2 iff n is prime.

a(n) = n iff mu(n) = 1.

Extensions

More terms from Amiram Eldar, May 18 2025