|
|
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
|
|
|
|