A129795 -id:A129795 - cp's OEIS frontend

A138258 Smallest positive integer m such that n divides [5^m/m] (=A129795(m)).

1, 2, 2, 2, 1, 2, 6, 7, 7, 7, 22, 2, 4, 6, 7, 13, 16, 7, 10, 7, 6, 31, 55, 7, 5, 4, 19, 6, 15, 7, 6, 17, 31, 16, 13, 7, 36, 10, 4, 7, 3, 6, 42, 31, 7, 55, 51, 13, 43, 26, 16, 4, 52, 19, 31, 13, 18, 15, 27, 7, 31, 6, 13, 17, 17, 31, 9, 16, 67, 13, 11, 7, 66, 36, 26, 18, 31, 4, 9, 13, 56, 61

Offset: 1

Max Alekseyev, Mar 09 2008

nonn

This sequence is well-defined.

Robert Israel, Table of n, a(n) for n = 1..10000
Romanian Master in Mathematics Contest, Problem 3, Bucharest, 2007.

Cf. A129795, A138255, A138256, A138257, A138259, A138260, A138261, A138262, A138263.

N:= 100: # for a(1)..a(N)
V:= Vector(N):
count:= 0: missing:= {$1..N}:
Q:= ilcm(seq(i,i=1..N)):
for m from 1 while count < N do
  v:= floor(5^m/m);
  r:= igcd(v,Q);
  d:= select(t -> r mod t = 0, missing);
  missing:= missing minus d;
  count:= count+nops(d);
  V[convert(d,list)]:= m;
od:
convert(V,list); # Robert Israel, Aug 27 2020

a[n_]:=Module[{m=1},While[!Divisible[Floor[5^m/m],n],m++];m];Array[a,82] (* James C. McMahon, Jun 05 2025 *)

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.

A225586 Floor((5^n-1)/n).

Original entry on oeis.org

4, 12, 41, 156, 624, 2604, 11160, 48828, 217013, 976562, 4438920, 20345052, 93900240, 435965401, 2034505208, 9536743164, 44878791360, 211927625868, 1003867701480, 4768371582031, 22706531343005, 108372081409801, 518301258916440, 2483526865641276

Offset: 1

Vincenzo Librandi, May 30 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A024049, A034474, A082482, A129795.

Magma
```
[Floor((5^n-1)/n): n in [1..30]];
```

Table[Floor[(5^n - 1) / n], {n, 30}] (* or *) Table[Quotient[5^n - 1, n], {n, 30}]

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

A138258 Smallest positive integer m such that n divides [5^m/m] (=A129795(m)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

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

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A225586 Floor((5^n-1)/n).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

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

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Mathematica

PARI