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

1,2

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.

Links

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

Example

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.

Prog

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

Crossrefs

Cf. A191614, A309243.

Sequence in context: A339132 A064895 A120877 * A174091 A318789 A328841

Adjacent sequences: A326301 A326302 A326303 * A326305 A326306 A326307

Keyword

nonn,mult

Author

Rémy Sigrist, Oct 17 2019

Status

approved