A339489 T(n, k) = Product(divisors(k) union {k*j : j = 2..floor(n/k)}). Triangle read by rows.

1, 2, 2, 6, 2, 3, 24, 8, 3, 8, 120, 8, 3, 8, 5, 720, 48, 18, 8, 5, 36, 5040, 48, 18, 8, 5, 36, 7, 40320, 384, 18, 64, 5, 36, 7, 64, 362880, 384, 162, 64, 5, 36, 7, 64, 27, 3628800, 3840, 162, 64, 50, 36, 7, 64, 27, 100, 39916800, 3840, 162, 64, 50, 36, 7, 64, 27, 100, 11

Offset: 1

Author

Peter Luschny, Dec 31 2020

Keywords

• nonn
• tabl

Comments

For the connection with paths in the divisor graph of {1,...,n} see the comment in A339492.

Examples

			The triangle starts:
[1]                            1;
[2]                           2, 2;
[3]                         6, 2, 3;
[4]                       24, 8, 3, 8;
[5]                     120, 8, 3, 8, 5;
[6]                  720, 48, 18, 8, 5, 36;
[7]                5040, 48, 18, 8, 5, 36, 7;
[8]             40320, 384, 18, 64, 5, 36, 7, 64;
[9]          362880, 384, 162, 64, 5, 36, 7, 64, 27;
[10]      3628800, 3840, 162, 64, 50, 36, 7, 64, 27, 100;
		

Crossrefs

T(n, 1) = A000142(n), T(n, n) = A007955(n).

Cf. A339491, A339492, A339496.

Programs

Maple

t := (n, k) -> NumberTheory:-Divisors(k) union {seq(k*j, j=2..n/k)}:
T := (n, k) -> mul(j, j = t(n, k)):
for n from 1 to 10 do seq(T(n, k), k=1..n) od;