A339489 - OEIS

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

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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