A193759 Array, by antidiagonals, A(k,n) is the number of prime factors of n^(2^k) + 1, counted with multiplicity.

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

Offset

0,10

Comments

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.

Links

Table of n, a(n) for n=0..82.

Example

A(4,5) = 3 because 1+5^16 = 152587890626 = 2 * 2593 * 29423041, which has 3 prime factors. The array begins:
================================================================
....|n=0|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|n=9|.10|.11|comment
====|===|===|===|===|===|===|===|===|===|===|===|===|===========
k=0.|.0.|.1.|.1.|.2.|.1.|.2.|.1.|.3.|.2.|.2.|.1.|.3.|A001222
k=1.|.0.|.1.|.1.|.2.|.1.|.2.|.1.|.3.|.2.|.2.|.1.|.2.|A193330
k=2.|.0.|.1.|.1.|.2.|.1.|.2.|.1.|.2.|.2.|.3.|.2.|.2.|A193929
k=3.|.0.|.1.|.1.|.3.|.1.|.3.|.2.|.3.|.3.|.2.|.2.|.3.|A194003
k=4.|.0.|.1.|.1.|.2.|.2.|.3.|.3.|.3.|.3.|.2.|.5.|.3.|not in OEIS
k=5.|.0.|.1.|.2.|.2.|.2.|.4.|.3.|.4.|.3.|.2.|.4.|.4.|not in OEIS
================================================================

Crossrefs

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

Sequence in context: A263848 A348157 A108455 * A117468 A340453 A116374

Adjacent sequences: A193756 A193757 A193758 * A193760 A193761 A193762

Keyword

nonn,hard,tabl

Author

Jonathan Vos Post, Aug 11 2011

Extensions

Edited by Alois P. Heinz, Aug 11 2011

More terms from Max Alekseyev, Sep 09 2011

Status

approved