A193759 - OEIS

%I #38 Mar 30 2012 18:40:59

%S 0,0,1,0,1,1,0,1,1,2,0,1,1,2,1,0,1,1,3,1,2,0,1,2,2,1,2,1,0,1,2,2,2,3,

%T 1,3,0,1,2,2,2,3,2,2,2,0,1,2,6,2,4,3,3,2,2,0,1,3,5,2,4,3,3,3,3,1,3,0,

%U 1,4,7,3,4,3,4,3,2,2,2,1,0,1,5

%N Array, by antidiagonals, A(k,n) is the number of prime factors of n^(2^k) + 1, counted with multiplicity.

%C The main diagonal A(n,n) = number of prime factors of n^(2^n) + 1, counted with multiplicity, begins 0, 1, 1, 3, 2, 4, 3, 6, 6.

%e A(4,5) = 3 because 1+5^16 = 152587890626 = 2 * 2593 * 29423041, which has 3 prime factors. The array begins:

%e ================================================================

%e ....|n=0|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|n=9|.10|.11|comment

%e ====|===|===|===|===|===|===|===|===|===|===|===|===|===========

%e k=0.|.0.|.1.|.1.|.2.|.1.|.2.|.1.|.3.|.2.|.2.|.1.|.3.|A001222

%e k=1.|.0.|.1.|.1.|.2.|.1.|.2.|.1.|.3.|.2.|.2.|.1.|.2.|A193330

%e k=2.|.0.|.1.|.1.|.2.|.1.|.2.|.1.|.2.|.2.|.3.|.2.|.2.|A193929

%e k=3.|.0.|.1.|.1.|.3.|.1.|.3.|.2.|.3.|.3.|.2.|.2.|.3.|A194003

%e k=4.|.0.|.1.|.1.|.2.|.2.|.3.|.3.|.3.|.3.|.2.|.5.|.3.|not in OEIS

%e k=5.|.0.|.1.|.2.|.2.|.2.|.4.|.3.|.4.|.3.|.2.|.4.|.4.|not in OEIS

%e ================================================================

%Y Cf. A001222, A002523, A060890, A193330, A193929, A194003.

%K nonn,hard,tabl

%O 0,10

%A _Jonathan Vos Post_, Aug 11 2011

%E Edited by _Alois P. Heinz_, Aug 11 2011

%E More terms from _Max Alekseyev_, Sep 09 2011