A104518 -id:A104518 - cp's OEIS frontend

A104524 Number of distinct prime divisors of 55...557 (with n 5s).

2, 1, 1, 2, 1, 3, 3, 3, 1, 3, 2, 5, 3, 1, 4, 3, 3, 3, 4, 2, 1, 2, 7, 4, 4, 4, 4, 5, 4, 4, 3, 2, 3, 5, 3, 4, 3, 7, 2, 4, 2, 4, 4, 8, 2, 4, 3, 6, 3, 2, 4, 7, 7, 7, 5, 5, 6, 7, 2, 4, 6, 3, 5, 5, 2, 5, 2, 4, 5, 5, 3, 9, 10, 6, 5, 6, 4, 4, 4, 5, 4, 5, 3, 6, 6, 4, 1

Offset: 1

Parthasarathy Nambi, Apr 20 2005

			The number of distinct prime divisors of 57 is 2.
The number of distinct prime divisors of 557 is 1 (prime).
The number of distinct prime divisors of 5557 is 1 (prime).

Amiram Eldar, Table of n, a(n) for n = 1..192

Cf. A104484, A104483, A104518.

Cf. A001221, A178769.

A104524 := proc(n) local x ;x := [7,seq(5,k=1..n)] ; add(op(i,x)*10^(i-1),i=1..nops(x)) ; numtheory[factorset](%) ; nops(%) ; end proc: # R. J. Mathar, Aug 24 2011

Table[PrimeNu[(50*10^n + 13)/9], {n, 1, 50}](* G. C. Greubel, May 07 2017 *)
Table[PrimeNu[FromDigits[PadLeft[{7},n,5]]],{n,2,90}] (* Harvey P. Dale, Dec 03 2021 *)

a(n) = omega((5*10^(n+1)+13)/9); \\ Michel Marcus, May 08 2017

a(n) = A001221(A178769(n+1)). - R. J. Mathar, Aug 24 2011

More terms from Michel Marcus, May 08 2017

More terms from Amiram Eldar, Jan 25 2020

A104660 Number of distinct prime divisors of 44...443 (with n 4s).

Original entry on oeis.org

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

Offset: 1

Parthasarathy Nambi, Apr 21 2005

			The number of distinct prime divisors of 43 is 1 (prime).
The number of distinct prime divisors of 443 is 1 (prime).
The number of distinct prime divisors of 4443 is 2.

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

Cf. A001221, A104518, A173770.

A104660 := proc(n) x := [3,seq(4,k=1..n)] ; add(op(i,x)*10^(i-1),i=1..nops(x)) ; numtheory[factorset](%) ; nops(%) ; end proc:
seq(A104660(n),n=1..45) ; # R. J. Mathar, Aug 23 2011

Table[PrimeNu[FromDigits[Join[Table[4, {n}], {3}]]], {n, 50}] (* Alonso del Arte, Aug 23 2011 *)
Table[PrimeNu[FromDigits[PadLeft[{3},n,4]]],{n,2,70}] (* Harvey P. Dale, Aug 22 2016 *)

a(n) = A001221(A173770(n+1)). - Amiram Eldar, Jan 25 2020

More terms from R. J. Mathar and Alonso del Arte, Aug 23 2011

More terms from Amiram Eldar, Jan 25 2020

A105973 Number of distinct prime divisors of 88...883 (with n 8's).

Original entry on oeis.org

1, 1, 1, 3, 1, 2, 2, 1, 1, 5, 2, 3, 3, 2, 1, 4, 2, 2, 3, 2, 3, 6, 3, 2, 2, 4, 3, 8, 3, 5, 3, 3, 4, 5, 4, 4, 6, 4, 2, 4, 4, 5, 4, 6, 5, 7, 4, 5, 4, 2, 1, 5, 3, 2, 5, 4, 5, 4, 4, 3, 4, 2, 4, 8, 4, 5, 2, 5, 5, 5, 1, 2, 6, 5, 4, 5, 1, 2, 7, 3, 4, 9, 6, 7, 7, 4, 4, 3, 4, 5, 6, 6, 7, 5, 4, 3, 5, 5, 2, 6

Offset: 0

Parthasarathy Nambi, Apr 28 2005

			The number of distinct prime divisors of 83 is 1 (prime).
The number of distinct prime divisors of 883 is 1 (prime).
The number of distinct prime divisors of 8883 is 3.

Amiram Eldar, Table of n, a(n) for n = 0..201

Cf. A104660, A104518, A104660.

Table[PrimeNu[FromDigits[PadLeft[{3},n,8]]],{n,100}] (* Harvey P. Dale, Mar 08 2015 *)

a(n) = omega((8*10^(n+1)-53)/9); \\ Michel Marcus, Jan 27 2014

a(n) = A001221(A173811(n+1)). - Michel Marcus, Jan 27 2014

cp's OEIS Frontend

A104524 Number of distinct prime divisors of 55...557 (with n 5s).

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A104660 Number of distinct prime divisors of 44...443 (with n 4s).

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A105973 Number of distinct prime divisors of 88...883 (with n 8's).

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Mathematica

PARI

Formula