A340008 a(n) is the image of n under the map: n -> n/2 if n is even, n-> n^2 - 1 if n is an odd prime, otherwise n -> n - 1.

0, 1, 8, 2, 24, 3, 48, 4, 8, 5, 120, 6, 168, 7, 14, 8, 288, 9, 360, 10, 20, 11, 528, 12, 24, 13, 26, 14, 840, 15, 960, 16, 32, 17, 34, 18, 1368, 19, 38, 20, 1680, 21, 1848, 22, 44, 23, 2208, 24, 48, 25, 50, 26, 2808, 27, 54, 28, 56, 29, 3480, 30, 3720, 31, 62, 32

Offset: 1

Author

Ya-Ping Lu, Dec 26 2020

Keywords

• nonn

Comments

This map is used in A339991.

Crossrefs

Cf. A339991.

Programs

Mathematica

Array[Which[EvenQ@ #, #/2, PrimeQ@ #, #^2 - 1, True, # - 1] &, 64] (* Michael De Vlieger, Dec 28 2020 *)

PARI

a(n) = if (n%2, if (isprime(n), n^2-1, n-1), n/2); \\ Michel Marcus, Dec 26 2020

Python

from sympy import isprime
for n in range(1, 1001):
    if n%2 == 0: a = n/2
    elif isprime(n) == 1: a = n*n - 1
    else: a = n - 1
    print(a)