A326304 Multiplicative with a(p^k) = a(p-1)^k + 1 for any k > 0 and any prime number p.

1, 2, 3, 2, 3, 6, 7, 2, 5, 6, 7, 6, 7, 14, 9, 2, 3, 10, 11, 6, 21, 14, 15, 6, 5, 14, 9, 14, 15, 18, 19, 2, 21, 6, 21, 10, 11, 22, 21, 6, 7, 42, 43, 14, 15, 30, 31, 6, 37, 10, 9, 14, 15, 18, 21, 14, 33, 30, 31, 18, 19, 38, 35, 2, 21, 42, 43, 6, 45, 42, 43, 10

Offset: 1

Author

Rémy Sigrist, Oct 17 2019

Keywords

• nonn
• mult

Comments

The sequence is well defined as computing a(p^k) involves terms of the form a(q) with q < p.

The fixed points are the divisors of 1806 = 2 * 3 * 7 * 43; they correspond to the first 16 terms of A191614.

Examples

			a(2) = a(1) + 1 = 1 + 1 = 2.
a(3) = a(2) + 1 = 2 + 1 = 3.
a(7) = a(6) + 1 = a(2)*a(3) + 1 = 2 * 3 + 1 = 7.
a(43) = a(42) + 1 = a(2)*a(3)*a(7) + 1 = 2*3*7 + 1 = 43.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A191614, A309243.

Programs

PARI

a(n) = my (f=factor(n)); prod (i=1, #f~, a(f[i,1]-1)^f[i,2]+1)