A104659 Number of distinct prime divisors of 44...441 (with n 4s).

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..199

Dario Alpern, Factorization using the Elliptic Curve Method

Makoto Kamada, Factorizations of 44...441.

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

Cf. A001221, A104564, A104517, A104484, A173768.

Sequence in context: A029550 A091110 A339660 * A077197 A320510 A117173

Adjacent sequences: A104656 A104657 A104658 * A104660 A104661 A104662

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