A103164 Integers but with the primes squared.

0, 1, 4, 9, 4, 25, 6, 49, 8, 9, 10, 121, 12, 169, 14, 15, 16, 289, 18, 361, 20, 21, 22, 529, 24, 25, 26, 27, 28, 841, 30, 961, 32, 33, 34, 35, 36, 1369, 38, 39, 40, 1681, 42, 1849, 44, 45, 46, 2209, 48, 49, 50, 51, 52, 2809, 54, 55, 56, 57, 58, 3481, 60, 3721, 62, 63, 64

Offset: 0

Author

Parthasarathy Nambi, Mar 17 2005

Keywords

• easy
• nonn

Comments

Möbius transform of A380444(n) (n>0). - Wesley Ivan Hurt, Jun 21 2025

Examples

			a(4) = 4 because 4 is composite.
a(5) = 25 because 5 is prime and 5^2 = 25.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000005, A010051.

Programs

Magma

[0] cat [IsPrime(n) select n^2 else n: n in [1..70]]; // Vincenzo Librandi, Feb 17 2017

Mathematica

Table[ If[ !PrimeQ[n], n, n^2], {n, 0, 64}] (* Robert G. Wilson v, Mar 19 2005 *)

Formula

a(n) = (n! mod n^2) + n, n>0, n != 4. - Gary Detlefs, Feb 21 2011

From Wesley Ivan Hurt, Jun 21 2025: (Start)

a(n) = n + n*(n-1)*c(n) where c = A010051 (n>0).

a(n) = n^tau(n^c(n)), where c = A010051 (n>0).

a(n) = Sum_{d|n} A380444(d) * mu(n/d), (n>0). (End)

Extensions

More terms from Robert G. Wilson v, Mar 19 2005