A194003 -id:A194003

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A193759

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

+10
0

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

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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.

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

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