

A326304


Multiplicative with a(p^k) = a(p1)^k + 1 for any k > 0 and any prime number p.


1



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
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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: A300500 A064895 A120877 * A174091 A318789 A328841
Adjacent sequences: A326301 A326302 A326303 * A326305 A326306 A326307


KEYWORD

nonn,mult


AUTHOR

Rémy Sigrist, Oct 17 2019


STATUS

approved



