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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.
From Robert Israel, Feb 23 2017: (Start)
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
(PARI) a(n)=bigomega(10^(n+1)*(10^(n+3)+666)+1) \\ Charles R Greathouse IV, Nov 26 2013
(Magma) [&+[p[2]: p in Factorization(666*10^(n+1)+100^(n+2)+1)]: n in [0..40]]; // Bruno Berselli, Nov 27 2013
CROSSREFS
Cf. A001913, A232448 (indices of Belphegor primes), A232449 (Belphegor numbers), A232450 (largest prime factor of A232449(n)).
Sequence in context: A299393 A299194 A300030 * A299451 A300089 A298230
KEYWORD
nonn,more
AUTHOR
Stanislav Sykora, Nov 24 2013
EXTENSIONS
a(45)-a(64) from Amiram Eldar, Apr 11 2020
STATUS
approved

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Last modified December 4 07:54 EST 2023. Contains 367557 sequences. (Running on oeis4.)