cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

Parthasarathy Nambi, Apr 20 2005

Keywords

Comments

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

Examples

			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.

Links

Crossrefs

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).

Programs

  • Mathematica
    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 *)

Formula

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

Extensions

More terms from Stefan Steinerberger, Mar 01 2006
Offset corrected and more terms added by Amiram Eldar, Jan 24 2020

A104517 Number of distinct prime divisors of 55...1 (with n 5s).

Original entry on oeis.org

2, 2, 3, 2, 2, 2, 3, 2, 5, 4, 1, 1, 3, 2, 5, 3, 4, 2, 4, 5, 4, 5, 3, 2, 3, 3, 3, 5, 3, 4, 6, 4, 4, 2, 4, 4, 3, 3, 5, 2, 2, 3, 2, 3, 7, 4, 3, 2, 5, 4, 4, 4, 6, 4, 8, 5, 3, 4, 7, 3, 2, 3, 4, 4, 5, 5, 5, 5, 6, 3, 5, 4, 2, 4, 4, 6, 4, 3, 2, 2, 6, 3, 5, 7, 5, 3, 6, 3, 4, 6, 7, 7
Offset: 1

Views

Author

Parthasarathy Nambi, Apr 19 2005

Keywords

Comments

Number of distinct prime factors of (10^(n + 1) - 1)*5/9 - 4. - Stefan Steinerberger, Mar 06 2006

Examples

			The number of distinct prime divisors of 51 is 2 which is the first term in the sequence.
The number of distinct prime divisors of 551 is 2 which is the second term in the sequence.
The number of distinct prime divisors of 5551 is 3 which is the third term in the sequence.

Links

Crossrefs

Cf. A001221, A056684 (a(n)=1), A104484, A173804.

Programs

  • Magma
    [#PrimeDivisors((10^(n+1)-1)*5 div 9-4): n in [1..80]]; // Vincenzo Librandi, Mar 09 2018
  • Maple
    f:= n -> nops(numtheory:-factorset( (10^(n + 1) - 1)*5/9 - 4)):
map(f, [$1..92]); # Robert Israel, Mar 08 2018
  • Mathematica
    Table[Length[FactorInteger[(10^(n + 1) - 1)*5/9 - 4]], {n, 1, 50}] (* Stefan Steinerberger, Mar 06 2006 *)
  • PARI
    a(n) = omega((10^(n + 1) - 1)*5/9 - 4); \\ Michel Marcus, Mar 09 2018

Formula

a(n) = A001221(A173804(n+1)). - Amiram Eldar, Jan 24 2020

Extensions

More terms from Stefan Steinerberger, Mar 06 2006
a(51)-a(92), and offset corrected, by Robert Israel, Mar 08 2018

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

Views

Author

Parthasarathy Nambi, Apr 21 2005, extended Aug 08 2010

Keywords

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

Examples

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

Links

Crossrefs

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

Programs

  • 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 *)

Formula

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

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Parthasarathy Nambi, Apr 20 2005

Keywords

Examples

			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).

Links

Crossrefs

Cf. A104484, A104483, A104518.
Cf. A001221, A178769.

Programs

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

Formula

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

Extensions

More terms from Michel Marcus, May 08 2017
More terms from Amiram Eldar, Jan 25 2020

A104543 Number of distinct prime divisors of 55...559 (with n 5s).

Original entry on oeis.org

1, 2, 3, 2, 2, 3, 1, 2, 4, 3, 1, 3, 3, 2, 4, 4, 1, 3, 3, 2, 4, 4, 4, 5, 1, 5, 4, 5, 4, 5, 1, 2, 4, 5, 5, 4, 2, 2, 3, 4, 3, 4, 4, 3, 5, 2, 5, 5, 3, 3, 6, 4, 2, 5, 4, 6, 2, 5, 4, 3, 4, 4, 6, 5, 5, 7, 3, 5, 5, 3, 4, 6, 5, 8, 3, 5, 5, 5, 2, 4, 4, 3, 4, 5, 3, 7, 6
Offset: 1

Views

Author

Parthasarathy Nambi, Apr 20 2005

Keywords

Examples

			The number of distinct prime divisors of 59 is 1 (prime).
The number of distinct prime divisors of 559 is 2.
The number of distinct prime divisors of 5559 is 3.

Links

Crossrefs

Cf. A104484, A104483.

Programs

  • Maple
    A104543 := proc(n) local x ;x := [9,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
  • Mathematica
    Table[PrimeNu[(50*10^n + 31)/9], {n,0,50}] (* G. C. Greubel, May 10 2017 *)
Table[PrimeNu[FromDigits[PadLeft[{9},n,5]]],{n,2,90}] (* Harvey P. Dale, Apr 22 2020 *)

Formula

a(n) = A001221((31+50*10^n)/9). - R. J. Mathar, Aug 24 2011

Extensions

More terms from Amiram Eldar, Jan 25 2020

A105267 a(n) = the number of divisors of 33...31, with n 3s.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 8, 8, 16, 4, 4, 8, 2, 8, 24, 8, 4, 16, 8, 8, 4, 16, 8, 8, 6, 8, 16, 64, 4, 4, 8, 8, 16, 16, 2, 8, 8, 64, 64, 8, 4, 8, 32, 8, 2, 8, 8, 16, 64, 8, 8, 32, 8, 32, 2, 8, 64, 32, 16, 8, 32, 8, 8, 32, 16, 64, 64, 8, 64, 4, 4, 16, 2
Offset: 0

Views

Author

Parthasarathy Nambi, Apr 29 2005

Keywords

Comments

The first seven 33...31 numbers are prime, so those terms are 2. - Don Reble, Oct 26 2006

Links

Crossrefs

Cf. A000005, A051200, A033175, A104484.

Programs

  • Mathematica
    a[n_] := DivisorSigma[0, (10^(n + 1) - 7)/3]; Array[a, 30, 0] (* Amiram Eldar, May 13 2020 *)
  • PARI
    a(n) = numdiv((10^(n + 1) - 7)/3); \\ Michel Marcus, May 13 2020

Formula

a(n) = A000005(A033175(n)). - Amiram Eldar, May 13 2020

Extensions

More terms from Don Reble, Oct 26 2006
Showing 1-6 of 6 results.

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