

A232451


Number of prime divisors of (10^(n+3) + 666)*10^(n+1) + 1 (see A232449) counted with multiplicity.


2



1, 2, 2, 3, 4, 3, 5, 4, 2, 5, 5, 4, 3, 1, 2, 3, 6, 4, 3, 6, 4, 2, 4, 5, 2, 4, 3, 6, 7, 7, 4, 3, 2, 4, 5, 3, 4, 7, 4, 6, 6, 4, 1, 4, 5, 4, 6, 6, 5, 3, 6, 4, 6, 6, 4, 11, 6, 6, 6, 4, 5, 5, 2, 6, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

The Belphegor numbers (A232449), though large and rarely prime (A232448), tend to contain only very few prime factors. One wonders whether this sequence might be bounded.
The sequence is unbounded.
Indeed, if p is in A001913 such that the polynomial 10^4 x^2 + 6660 x + 1 has a simple root mod p, then for all k there exist Belphegor numbers divisible by p^k.
For example, p=29 works; we have A232449(n) divisible by 29^k for n = 6, 158, 5522, 41570, 8153130, 107172470, 3553045502, 136793469406, 2761185750502, 142830181379582, ...
(End)


LINKS



MAPLE

seq(numtheory:bigomega(10^(2*n+4)+666*10^(n+1)+1), n=0..30); # Robert Israel, Feb 23 2017


MATHEMATICA

Table[Total[Transpose[FactorInteger[(10^(n + 3) + 666)*10^(n + 1) + 1]][[2]]], {n, 0, 25}] (* T. D. Noe, Nov 28 2013 *)


PROG

(Magma) [&+[p[2]: p in Factorization(666*10^(n+1)+100^(n+2)+1)]: n in [0..40]]; // Bruno Berselli, Nov 27 2013


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



