A354258 Earliest occurrence of n in A354257.

1, 3, 9, 16, 25, 36, 49, 32, 27, 75, 121, 144, 169, 147, 225, 64, 289, 108, 361, 400, 441, 363, 529, 288, 125, 507, 81, 784, 841, 900, 961, 128, 1089, 867, 1225, 432, 1369, 1083, 1521, 800, 1681, 1764, 1849, 1936, 675, 1587, 2209, 576, 343, 375, 2601, 2704

Offset: 1

Author

Jianing Song, May 21 2022

Keywords

• nonn
• easy

Comments

a(n) is odd if and only if n is odd or n == 2, 10 (mod 12).

a(n) = n^2 if and only if: (a) n is odd or n == 6 (mod 12), and n is squarefree; or (b) n is 4 times an odd squareefree number.

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A354257, A007947, A354270.

Programs

PARI

rad(n) = factorback(factorint(n)[, 1]);
a(n) = n*rad(n)*if(n%2 || n%12==6, 1, if(n%12==2 || n%12==10, 3/4, 2))

Formula

a(n) = n * rad(n) if n is odd or n == 6 (mod 12); (3/4) * n * rad(n) if n == 2, 10 (mod 12); 2 * n * rad(n) if n is divisible by 4, where rad = A007947.