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 1-3 of 3 results.

A110753 a(n) is the number of divisors of the concatenation of 2178 with itself n times.

Original entry on oeis.org

18, 72, 384, 288, 576, 3072, 1152, 9216, 7680, 9216, 6144, 24576, 2304, 18432, 3145728, 147456, 4608, 491520, 288, 147456, 9437184, 98304, 4608, 12582912, 589824, 36864, 1179648, 589824, 36864, 201326592
Offset: 1

Views

Author

Amarnath Murthy, Aug 11 2005

Keywords

Comments

2178 has the property that any number of concatenations of it with itself and its digit reversal have the same set of distinct prime factors.

Examples

			a(2) = tau(21782178) = 72.

Crossrefs

Cf. A110751, A110752.

Programs

  • Mathematica
    k = 0; Do[k = (10^4 * k) + 2178; Print[DivisorSigma[0, k]], {n, 1, 30}] (* Ryan Propper, Aug 28 2005 *)
Table[DivisorSigma[0,FromDigits[PadRight[{},4n,{2,1,7,8}]]],{n,30}] (* Harvey P. Dale, Jun 23 2014 *)

Extensions

More terms from Ryan Propper, Aug 28 2005

A110754 a(n) = tau(N), where N = the number obtained as a concatenation of 8712 with itself n times and tau(n) = number of divisors of n.

Original entry on oeis.org

36, 144, 768, 576, 1152, 6144, 2304, 18432, 15360, 18432, 12288, 49152, 4608, 36864, 6291456, 294912, 9216, 983040, 576, 294912, 18874368, 196608, 9216, 25165824, 1179648, 73728, 2359296, 1179648, 73728, 402653184, 2304, 2359296, 33554432, 147456, 75497472, 31457280, 147456, 36864
Offset: 1

Views

Author

Amarnath Murthy, Aug 11 2005

Keywords

Comments

8712 has the property that any number of concatenation of it with self and the digit reversal have same prime divisors.

Examples

			a(2) = tau(87128712) = 144.

Crossrefs

Cf. A110751, A110752, A110753.

Programs

  • Maple
    A110754 := proc(n) local pow8712,i ; pow8712 := 8712*add(10^(4*i),i=0..n-1) ; numtheory[tau](pow8712) ; end: seq(A110754(n),n=1..22) ; # R. J. Mathar, Aug 17 2007
  • Mathematica
    Table[DivisorSigma[0,FromDigits[PadRight[{},4n,{8,7,1,2}]]],{n,25}] (* Harvey P. Dale, Dec 29 2016 *)
  • PARI
    a(n)={numdiv(8712*(10^(4*n)-1)/9999)} \\ Andrew Howroyd, Nov 09 2019

Formula

a(n) = A000005(8712*Sum_{i=0..n-1} 10^(4i)). - R. J. Mathar, Aug 17 2007

Extensions

More terms from R. J. Mathar, Aug 17 2007
a(23)-a(38) from Andrew Howroyd, Nov 09 2019

A110755 a(n) = Tau(N), where N = the number obtained as a concatenation of 9801 with itself n times. Tau(n) = number of divisors of n.

Original entry on oeis.org

15, 60, 288, 240, 480, 2304, 960, 7680, 5376, 7680, 5120, 18432, 1920, 15360, 2359296, 122880, 3840, 344064, 240, 122880, 7077888, 81920, 3840, 9437184, 491520, 30720, 786432, 491520, 30720, 150994944, 960, 983040, 12582912, 61440
Offset: 1

Views

Author

Amarnath Murthy, Aug 11 2005

Keywords

Comments

9801, has the property that any number of concatenation of it with self and the digit reversal have same prime divisors.

Examples

			a(2) =tau(98019801) = 60.

Crossrefs

Cf. A110751, A110752, A110753, A110754.

Extensions

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
More terms from David Wasserman, Dec 18 2008
Showing 1-3 of 3 results.

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