A334216 -id:A334216 - cp's OEIS frontend

A334217 Irregular table T(n, k) read by rows, n > 0 and k = 1..A334216(n); n-th row corresponds to distinct terms of n-th row of A334215, in ascending order.

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 6, 1, 7, 1, 2, 8, 1, 3, 9, 1, 10, 1, 11, 1, 2, 12, 1, 13, 1, 14, 1, 15, 1, 2, 4, 16, 1, 17, 1, 3, 18, 1, 19, 1, 2, 20, 1, 21, 1, 22, 1, 23, 1, 2, 24, 1, 5, 25, 1, 26, 1, 3, 27, 1, 2, 28, 1, 29, 1, 30, 1, 31, 1, 2, 4, 32, 1, 33

Offset: 1

Rémy Sigrist, Apr 19 2020

			The first rows are:
  n     n-th row
  --    -------------
   1    [1]
   2    [1, 2]
   3    [1, 3]
   4    [1, 2, 4]
   5    [1, 5]
   6    [1, 6]
   7    [1, 7]
   8    [1, 2, 8]
   9    [1, 3, 9]
  10    [1, 10]
  11    [1, 11]
  12    [1, 2, 12]
  13    [1, 13]
  14    [1, 14]
  15    [1, 15]
  16    [1, 2, 4, 16]

Cf. A000188, A261969, A334215, A334216.

row(n) = { my (f=factor(n)); Set(apply (k -> prod (i=1, #f~, f[i,1]^(f[i,2]\k)), [1..1+if (n==1, 0, vecmax(f[,2]~))])) }

T(n, 1) = 1.
T(n, 2) = A261969(n) for any n > 1.
T(n, A334216(n)-1) = A000188(n) for any n > 1.
T(n, A334216(n)) = n.

A334215 T(n, k) is the greatest positive integer m such that m^k divides n; square array T(n, k), n, k > 0 read by antidiagonals downwards.

Original entry on oeis.org

1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 2, 5, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2, 9, 1, 1, 1, 1, 1, 1, 1, 2, 3, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Rémy Sigrist, Apr 19 2020

			Square array starts:
  n\k|   1  2  3  4  5  6  7  8  9 10
  ---+-------------------------------
    1|   1  1  1  1  1  1  1  1  1  1
    2|   2  1  1  1  1  1  1  1  1  1
    3|   3  1  1  1  1  1  1  1  1  1
    4|   4  2  1  1  1  1  1  1  1  1
    5|   5  1  1  1  1  1  1  1  1  1
    6|   6  1  1  1  1  1  1  1  1  1
    7|   7  1  1  1  1  1  1  1  1  1
    8|   8  2  2  1  1  1  1  1  1  1
    9|   9  3  1  1  1  1  1  1  1  1
   10|  10  1  1  1  1  1  1  1  1  1
   11|  11  1  1  1  1  1  1  1  1  1
   12|  12  2  1  1  1  1  1  1  1  1
   13|  13  1  1  1  1  1  1  1  1  1
   14|  14  1  1  1  1  1  1  1  1  1
   15|  15  1  1  1  1  1  1  1  1  1
   16|  16  4  2  2  1  1  1  1  1  1

Cf. A000188, A051903, A053150, A053164, A060175, A261969, A334215, A334216.

T(n,k) = { my (f=factor(n)); prod (i=1, #f~, f[i,1]^(f[i,2]\k)) }

T(n, 1) = n.
T(n, 2) = A000188(n).
T(n, 3) = A053150(n).
T(n, 4) = A053164(n).
T(n, A051903(n)) = A261969(n).
T(n, k) = 1 for any k > A051903(n).
T(n^k, k) = n.

cp's OEIS Frontend

A334217 Irregular table T(n, k) read by rows, n > 0 and k = 1..A334216(n); n-th row corresponds to distinct terms of n-th row of A334215, in ascending order.

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