A060155 -id:A060155 - cp's OEIS frontend

A057075 Table read by antidiagonals of T(n,k)=floor(n^n/k) with n,k >= 1.

1, 0, 4, 0, 2, 27, 0, 1, 13, 256, 0, 1, 9, 128, 3125, 0, 0, 6, 85, 1562, 46656, 0, 0, 5, 64, 1041, 23328, 823543, 0, 0, 4, 51, 781, 15552, 411771, 16777216, 0, 0, 3, 42, 625, 11664, 274514, 8388608, 387420489, 0, 0, 3, 36, 520, 9331, 205885, 5592405, 193710244, 10000000000

Offset: 1

Henry Bottomley, Jul 31 2000

			From _Seiichi Manyama_, Aug 12 2023: (Start)
Square array begins:
      1,     0,     0,     0,    0,    0, ...
      4,     2,     1,     1,    0,    0, ...
     27,    13,     9,     6,    5,    4, ...
    256,   128,    85,    64,   51,   42, ...
   3125,  1562,  1041,   781,  625,  520, ...
  46656, 23328, 15552, 11664, 9331, 7776, ... (End)

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

Rows are: A000007 (essentially), A033324, A033347, A057066-A057074.
Columns include A000312 and A057065.
Leading diagonal is A000169.
Cf. A060155.

T(n, k) = n^n\k; \\ Seiichi Manyama, Aug 12 2023

A060154 Table T(n,k) by antidiagonals of n^k mod k [n,k >= 1].

Original entry on oeis.org

0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 4, 3, 0, 2, 0, 0, 1, 2, 3, 4, 1, 0, 1, 0, 1, 0, 3, 4, 0, 0, 1, 0, 0, 1, 8, 1, 4, 1, 1, 1, 2, 1, 0, 1, 4, 0, 0, 5, 0, 2, 0, 0, 0, 0, 1, 2, 9, 1, 1, 6, 1, 3, 1, 1, 1, 0, 1, 4, 3, 6, 8, 0, 0, 4, 4, 0, 2, 0, 0, 1, 2, 9, 4, 5, 0, 1, 1, 3, 0, 1, 0, 1, 0

Offset: 1

Henry Bottomley, Mar 12 2001

			T(5,3) = 5^3 mod 3 = 125 mod 3 = 2.
Rows start:
  0, 1, 1, 1, 1, ...
  0, 0, 2, 0, 2, ...
  0, 1, 0, 1, 3, ...
  0, 0, 1, 0, 4, ...
  0, 1, 2, 1, 0, ...

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

Rows include A057427, A015910, A056969.
Columns include A000004, A000035 (several times), A010872, A010874, A010876, A021559 and other periodic sequences.
Diagonals include A000004 and A057427.
Cf. A114448.

T(n, k) = A051129(n, k)-n*A060155(n, k).

A060156 a(n) = floor(10^n/n).

Original entry on oeis.org

10, 50, 333, 2500, 20000, 166666, 1428571, 12500000, 111111111, 1000000000, 9090909090, 83333333333, 769230769230, 7142857142857, 66666666666666, 625000000000000

Offset: 1

Henry Bottomley, Mar 12 2001

nonn

			a(6) = floor(1000000/6) = 166666.

Harry J. Smith, Table of n, a(n) for n = 1..200

Cf. A000799, A056159, A060155.

{ default(realprecision, 10); for (n=1, 200, write("b060156.txt", n, " ", floor(10^n/n)); ) } \\ Harry J. Smith, Jul 02 2009

a(n) = (A011557(n) - A056969(n))/n.

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A057075 Table read by antidiagonals of T(n,k)=floor(n^n/k) with n,k >= 1.

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A060154 Table T(n,k) by antidiagonals of n^k mod k [n,k >= 1].

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A060156 a(n) = floor(10^n/n).

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