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.

A138261 Smallest positive integer m such that n divides [8^m/m] (=A129798(m)).

Original entry on oeis.org

1, 1, 10, 1, 3, 10, 7, 1, 11, 3, 21, 11, 9, 9, 13, 2, 3, 11, 13, 9, 11, 21, 15, 11, 21, 9, 13, 9, 10, 13, 11, 2, 21, 3, 9, 11, 13, 13, 17, 9, 21, 11, 10, 21, 13, 15, 92, 55, 29, 21, 20, 9, 58, 13, 21, 9, 13, 10, 22, 13, 21, 11, 11, 4, 9, 21, 23, 9, 67, 9, 46, 11, 13, 13, 21, 13, 31, 17
Offset: 1

Views

Author

Max Alekseyev, Mar 09 2008

Keywords

Comments

This sequence is well-defined.

Links

  • Romanian Master in Mathematics Contest, Problem 3, Bucharest, 2007.

Crossrefs

Cf. A129798, A138255, A138256, A138257, A138258, A138259, A138260, A138262, A138263.

Programs

  • Mathematica
    spi[n_]:=Module[{m=1},While[!Divisible[Floor[8^m/m],n],m++];m]; Array[spi,80] (* Harvey P. Dale, Oct 23 2022 *)

Formula

If A138255(n) is divisible by 3 then a(n)=A138255(n)/3. In general, a(n) >= A138255(n)/3.

A060155 Table T(n,k) by antidiagonals of floor(n^k/k) [n,k >= 1].

Original entry on oeis.org

1, 0, 2, 0, 2, 3, 0, 2, 4, 4, 0, 4, 9, 8, 5, 0, 6, 20, 21, 12, 6, 0, 10, 48, 64, 41, 18, 7, 0, 18, 121, 204, 156, 72, 24, 8, 0, 32, 312, 682, 625, 324, 114, 32, 9, 0, 56, 820, 2340, 2604, 1555, 600, 170, 40, 10, 0, 102, 2187, 8192, 11160, 7776, 3361, 1024, 243, 50, 11
Offset: 1

Views

Author

Henry Bottomley, Mar 12 2001

Keywords

Examples

			T(5,3)=[5^3/3]=[125/3]=41.
Rows start:
  1,  0,  0,   0,   0, ...
  2,  2,  2,   4,   6, ...
  3,  4,  9,  20,  48, ...
  4,  8, 21,  64, 204, ...
  5, 12, 41, 156, 625, ...

Links

Crossrefs

Rows include A000007, A000799, A092763, A129794, A129795, A129796, A129797, A129798, A129799, A060156.
Columns include A000027, A007590.
Diagonals include A000169.

Formula

T(n, k) = (A051129(n, k)-A060154(n, k))/k.

A246003 Floor(m^n/n) with n >= m >= 1.

Original entry on oeis.org

1, 0, 2, 0, 2, 9, 0, 4, 20, 64, 0, 6, 48, 204, 625, 0, 10, 121, 682, 2604, 7776, 0, 18, 312, 2340, 11160, 39990, 117649, 0, 32, 820, 8192, 48828, 209952, 720600, 2097152, 0, 56, 2187, 29127, 217013, 1119744, 4483734, 14913080, 43046721, 0, 102, 5904, 104857
Offset: 1

Views

Author

Vincenzo Librandi, Dec 11 2014

Keywords

Examples

			Triangle begins:
1;
0,  2;
0,  2,    9;
0,  4,   20,    64;
0,  6,   48,   204,    625;
0, 10,  121,   682,   2604,    7776;
0, 18,  312,  2340,  11160,   39990,  117649;
0, 32,  820,  8192,  48828,  209952,  720600,  2097152;
0, 56, 2187, 29127, 217013, 1119744, 4483734, 14913080, 43046721;
...

Crossrefs

Cf. A117142.
Cf. for the k-th column: A063524 (k=1), A000799(k=2), A092763(k=3), A129794(k=4), A129795(k=5), A129796 (k=6), A129797 (k=7), A129798 (k=8), A129799 (k=9).

Programs

  • Magma
    /* As triangle: */ [[Floor(m^n/n): m in [1..n]]: n in [1..10]];
  • Mathematica
    Table[Floor[m^n/n], {n, 1, 10}, {m, 1, n}]
  • PARI
    tabl(nn) = {for (n=1, nn, for (m=1, n, print1(m^n\n, ", ");); print(););} \\ Michel Marcus, Dec 12 2014
Showing 1-3 of 3 results.

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