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.

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

1,3

Links

Table of n, a(n) for n=1..86.

Formula

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.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A167407 A216764 A165430 * A164823 A167269 A105535

Adjacent sequences: A334212 A334213 A334214 * A334216 A334217 A334218

Keyword

nonn,tabl

Author

Rémy Sigrist, Apr 19 2020

Status

approved