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A339489 T(n, k) = Product(divisors(k) union {k*j : j = 2..floor(n/k)}). Triangle read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

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;

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;

CROSSREFS

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

Cf. A339491, A339492, A339496.

Sequence in context: A281552 A205506 A110141 * A293443 A247765 A129750

Adjacent sequences:  A339486 A339487 A339488 * A339490 A339491 A339492

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 31 2020

STATUS

approved

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Last modified May 7 09:22 EDT 2021. Contains 343645 sequences. (Running on oeis4.)