A189102 -id:A189102 - cp's OEIS frontend

A189103 Least common multiple of n! and its arithmetic derivative.

0, 2, 30, 264, 7320, 30960, 1592640, 38183040, 394450560, 2238969600, 275106585600, 4038941491200, 689773321036800, 20996629900646400, 111964387062528000, 2210304446558208000, 642338416210563072000, 19249748121316737024000, 6980209591900198477824000

Offset: 1

Giorgio Balzarotti, Apr 16 2011

nonn

			n = 5: 5! = 120, 120' = 244, lcm(120,244) = 7320 -> a(5) = 7320

Nathaniel Johnston, Table of n, a(n) for n = 1..200

Cf. A068311, A083346, A083346, A085731, A086130, A189100, A189102.

a(n) = lcm(n!,n!') = lcm(A000142(n),A068311(n)).

A188901 Integers in the sequences (arithmetic derivative of k) divided by k.

Original entry on oeis.org

0, 1, 2, 1, 3, 2, 4, 3, 2, 5, 4, 3, 1, 6, 5, 4, 2, 7, 3, 6, 5, 3, 8, 4, 2, 7, 6, 4, 9, 5, 3, 8, 4, 7, 5, 1, 10, 6, 4, 9, 5, 3, 8, 6, 2, 11, 7, 5, 10, 6, 4, 2, 9, 7, 3, 5, 12, 8, 6, 2, 11, 7, 5, 3, 10, 8, 4, 6, 4, 13, 9, 7, 3, 12, 8, 6, 4, 11

Offset: 1

Giorgio Balzarotti, Apr 16 2011

nonn

Integers in the sequence (k'/k) = A003415(k)/k. See A072873 for the values of k where k'/k is an integer.

			1' = 0, 0/1 = 0 -> a(1) = 0;
4' = 4 ,4/4 = 1 -> a(2) = 1;
16' = 32, 32/16 = 2 -> a(3) = 2.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 2500 terms from Nathaniel Johnston)

Cf. A003415, A068311, A072873, A083346, A083346, A085731, A086130, A189100, A189102.

cp's OEIS Frontend

A189103 Least common multiple of n! and its arithmetic derivative.

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