A326304 - OEIS

%I #14 Jan 18 2020 20:40:56

%S 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,

%T 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,

%U 21,14,33,30,31,18,19,38,35,2,21,42,43,6,45,42,43,10

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

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

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

%H Rémy Sigrist, <a href="/A326304/b326304.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = a(1) + 1 = 1 + 1 = 2.

%e a(3) = a(2) + 1 = 2 + 1 = 3.

%e a(7) = a(6) + 1 = a(2)*a(3) + 1 = 2 * 3 + 1 = 7.

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

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

%Y Cf. A191614, A309243.

%K nonn,mult

%O 1,2

%A _Rémy Sigrist_, Oct 17 2019