A104517 -id:A104517 - cp's OEIS frontend

A104564 Number of distinct prime divisors of 77...771 (with n 7's).

1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 1, 3, 4, 2, 2, 3, 2, 1, 4, 3, 1, 3, 3, 2, 3, 4, 2, 7, 1, 5, 6, 3, 3, 4, 3, 4, 5, 5, 3, 5, 4, 2, 3, 3, 6, 2, 2, 6, 5, 4, 3, 4, 4, 6, 2, 6, 5, 4, 4, 4, 5, 3, 3, 5, 2, 6, 3, 5, 5, 4, 6, 4, 6, 5, 3, 3, 4, 4, 4, 4, 6, 4, 3, 6, 5, 3

Offset: 1

Parthasarathy Nambi, Apr 20 2005

Also number of distinct prime factors of (10^(n + 1) - 1)*7/9 - 6. - Stefan Steinerberger, Mar 01 2006

			The number of distinct prime divisors of 71 is 1 (prime).
The number of distinct prime divisors of 771 is 2.
The number of distinct prime divisors of 7771 is 2.

Amiram Eldar, Table of n, a(n) for n = 1..231

Cf. A001221, A104484, A104483, A173806.

Cf. A104484 (3 instead of 7), A104659 (4 instead of 7), A104517 (5 instead of 7), A104890 (6 instead of 7), A105972 (8 instead of 7), A105259 (9 instead of 7).

Table[Length[FactorInteger[(10^(n + 1) - 1)*7/9 - 6]], {n, 1, 50}] (* Stefan Steinerberger, Mar 01 2006 *)
PrimeNu/@(FromDigits/@Table[PadLeft[{1},n,7],{n,2,55}])  (* Harvey P. Dale, Apr 22 2011 *)

a(n) = A001221(A173806(n+1)). - Amiram Eldar, Jan 24 2020

More terms from Stefan Steinerberger, Mar 01 2006

Offset corrected and more terms added by Amiram Eldar, Jan 24 2020

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

Original entry on oeis.org

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

Parthasarathy Nambi, Apr 21 2005, extended Aug 08 2010

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

			The number of distinct prime divisors of 441 is 2.
The number of distinct prime divisors of 44444444444444444444444444444441 is four.

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.

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

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 *)

a(n) = A001221(A173768(n+1)). - Amiram Eldar, Jan 24 2020

a(32) - a(105) from Robert G. Wilson v, Aug 09 2010

A105972 Number of distinct prime divisors of 88...881 (with n 8's).

Original entry on oeis.org

0, 1, 1, 2, 4, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 3, 8, 1, 3, 2, 2, 5, 2, 4, 6, 2, 2, 5, 3, 4, 4, 4, 2, 5, 5, 5, 4, 6, 3, 5, 3, 2, 5, 4, 4, 7, 4, 4, 6, 3, 5, 5, 3, 5, 6, 5, 5, 5, 4, 3, 5, 4, 2, 7, 3, 3, 8, 3, 5, 6, 7, 3, 6, 3, 3, 7, 3, 1, 5, 5, 4, 8, 4, 3, 4, 4

Offset: 0

Parthasarathy Nambi, Apr 28 2005

			The number of distinct prime divisors of 81 is 1.
The number of distinct prime divisors of 881 is 1 (prime).
The number of distinct prime divisors of 8881 is 2.

Amiram Eldar, Table of n, a(n) for n = 0..203

Cf. A001221, A104564, A104517, A104659, A173810.

Table[PrimeNu[(8*10^(n+1) - 71)/9], {n,0,50}] (* G. C. Greubel, May 16 2017 *)
PrimeNu/@Table[10 FromDigits[PadRight[{},n,8]]+1,{n,0,90}] (* Harvey P. Dale, Apr 25 2019 *)

a(n) = omega((8*10^(n+1)-71)/9); \\ Michel Marcus, Jan 27 2014

a(n) = A001221(A173810(n+1)). - Michel Marcus, Jan 27 2014

More terms from Michel Marcus, Jan 27 2014

cp's OEIS Frontend

A104564 Number of distinct prime divisors of 77...771 (with n 7's).

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

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A105972 Number of distinct prime divisors of 88...881 (with n 8's).

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