A129794 -id:A129794 - cp's OEIS frontend

A138257 Smallest positive integer m such that n divides [4^m/m] (=A129794(m)).

1, 1, 3, 1, 7, 5, 3, 2, 7, 7, 6, 5, 7, 13, 7, 4, 5, 7, 9, 7, 3, 6, 10, 22, 11, 7, 19, 13, 15, 7, 6, 4, 31, 5, 13, 7, 19, 20, 7, 22, 11, 13, 15, 31, 7, 24, 10, 69, 43, 11, 5, 7, 44, 19, 31, 26, 9, 15, 42, 7, 31, 6, 13, 4, 7, 31, 69, 5, 67, 13, 124, 26, 9, 19, 11, 20, 31, 7, 18, 69, 28, 11, 126

Offset: 1

Max Alekseyev, Mar 09 2008

nonn

This sequence is well-defined.

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

Cf. A129794, A138255, A138256, A138258, A138259, A138260, A138261, A138262, A138263.

spi[n_]:=Module[{m=1},While[!Divisible[Floor[4^m/m],n],m++];m]; Array[ spi,90] (* Harvey P. Dale, Sep 13 2020 *)

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

Henry Bottomley, Mar 12 2001

			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, ...

Seiichi Manyama, Antidiagonals n = 1..140, flattened

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

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

Vincenzo Librandi, Dec 11 2014

			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;
...

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).

/* As triangle: */ [[Floor(m^n/n): m in [1..n]]: n in [1..10]];

Table[Floor[m^n/n], {n, 1, 10}, {m, 1, n}]

tabl(nn) = {for (n=1, nn, for (m=1, n, print1(m^n\n, ", ");); print(););} \\ Michel Marcus, Dec 12 2014

cp's OEIS Frontend

A138257 Smallest positive integer m such that n divides [4^m/m] (=A129794(m)).

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

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

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