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

0,3

Comments

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

Links

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

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)

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A010051.

Sequence in context: A340769 A088377 A066048 * A210966 A300516 A178147

Adjacent sequences: A103161 A103162 A103163 * A103165 A103166 A103167

Keyword

easy,nonn

Author

Parthasarathy Nambi, Mar 17 2005

Extensions

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

Status

approved