A343881 - OEIS

A343881

Table read by antidiagonals upward: T(n,k) is the least integer m > k such that k^x * m^y = c^n for some positive integers c, x, and y where x < n and y < n; n >= 2, k >= 1.

4, 8, 8, 4, 4, 12, 32, 4, 9, 9, 4, 4, 9, 16, 20, 128, 4, 9, 8, 25, 24, 4, 4, 9, 8, 20, 36, 28, 8, 4, 9, 8, 25, 24, 49, 18, 4, 4, 9, 8, 20, 36, 28, 27, 16, 2048, 4, 9, 8, 25, 24, 49, 18, 24, 40, 4, 4, 9, 8, 20, 36, 28, 16, 12, 80, 44, 8192, 4, 9, 8, 25, 24, 49

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OFFSET

2,1

COMMENTS

For prime p, the p-th row consists of distinct integers.

Conjecture: T(p,k) = A064549(k) for fixed k > 1 and sufficiently large p.

LINKS

Table of n, a(n) for n=2..74.

FORMULA

T(n,1) = 2^A020639(n).

EXAMPLE

Table begins:

n\k| 1 2 3 4 5 6 7 8 9 10

-----+-----------------------------------------

2 | 4, 8, 12, 9, 20, 24, 28, 18, 16, 40

3 | 8, 4, 9, 16, 25, 36, 49, 27, 24, 80

4 | 4, 4, 9, 8, 20, 24, 28, 18, 12, 40

5 | 32, 4, 9, 8, 25, 36, 49, 16, 27, 100

6 | 4, 4, 9, 8, 20, 24, 28, 9, 16, 40

7 | 128, 4, 9, 8, 25, 36, 49, 16, 27, 100

8 | 4, 4, 9, 8, 20, 24, 28, 16, 12, 40

9 | 8, 4, 9, 8, 25, 36, 49, 16, 24, 80

10 | 4, 4, 9, 8, 20, 24, 28, 16, 16, 40

11 | 2048, 4, 9, 8, 25, 36, 49, 16, 27, 100

T(2, 3) = 12 with 3 * 12 = 6^2.

T(3,10) = 80 with 10^2 * 80 = 20^3.

T(4, 5) = 20 with 5^2 * 20^2 = 10^4.

T(5, 1) = 32 with 1 * 32 = 2^5.

T(6, 8) = 9 with 8^2 * 9^3 = 6^6.

CROSSREFS

Rows: A072905 (n=2), A277781 (n=3).

Cf. A064549, A343825.

Sequence in context: A319592 A200395 A064927 * A227896 A114610 A200390

Adjacent sequences: A343878 A343879 A343880 * A343882 A343883 A343884

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, May 02 2021

STATUS

approved