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A104659
Number of distinct prime divisors of 44...441 (with n 4s).
4
1, 2, 1, 2, 2, 2, 2, 4, 2, 1, 5, 3, 2, 6, 3, 3, 3, 3, 2, 4, 4, 4, 4, 4, 4, 5, 1, 2, 6, 4, 4, 6, 4, 4, 4, 5, 4, 8, 4, 4, 7, 3, 2, 7, 3, 7, 4, 6, 3, 4, 6, 2, 6, 1, 4, 7, 2, 5, 4, 4, 4, 6, 4, 2, 3, 6, 3, 5, 4, 3, 11, 5, 4, 4, 5, 7, 3, 4, 3, 5, 4, 4, 3, 3, 6, 8, 3, 4, 4, 2, 6, 6, 1, 7, 8, 4, 4, 7, 4, 6, 6, 4, 4, 5, 6
OFFSET
1,2
COMMENTS
There are very few primes in this sequence. 41 appears as the smallest prime divisor frequently. There are many semiprimes.
41 is prime.
4441 is prime.
44444 444441 is prime.
4444 444444 444444 444444 444441 is prime.
4444444444444444444444444444444444444444444444444444441 is prime.
Computed using www.alpertron.com.ar/ECM.HTM
FORMULA
a(n) = A001221(A173768(n+1)). - Amiram Eldar, Jan 24 2020
EXAMPLE
The number of distinct prime divisors of 441 is 2.
The number of distinct prime divisors of 44444444444444444444444444444441 is four.
MATHEMATICA
f[n_] := Length@ FactorInteger[(4*10^(n + 1) - 31)/9]; Array[f, 105] (* Robert G. Wilson v, Aug 09 2010 *)
PrimeNu/@Rest[FromDigits/@Table[PadLeft[{1}, n, 4], {n, 110}]] (* Harvey P. Dale, Mar 16 2012 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Parthasarathy Nambi, Apr 21 2005, extended Aug 08 2010
EXTENSIONS
a(32) - a(105) from Robert G. Wilson v, Aug 09 2010
STATUS
approved