(define (lawgin x) (apply lcm (iota x 1)))

1 ]=> (map lawgin (iota 20 1))

;Value: (1 2 6 12 60 60 420 840 2520 2520 27720 27720 360360 360360 360360 720720 12252240 12252240 232792560 232792560)

The ever obtuse and smug qbguy did get the correct answer, to his credit.

Each number is the least common multiple according to it's position in the sequence or, stated differently, each number is the smallest integer which is evenly divisible by all the integers up to it's position in the sequence.

1, 2, 6, 12, 60, 60, 420, 840, 2520

1 is the smallest integer evenly divisible by 1

2 is the smallest integer evenly divisible by 1 and 2

6 is the smallest integer evenly divisible by 1, 2, and 3

12 is the smallest integer evenly divisible by 1, 2, 3, and 4

etc.

Below is the code I used to produce the sequence, though it craps out after 22 terms due to an overflow.

CLS

DEFLNG A

DO

p = p + 1

DO

a = a + 1

IF p > 4 THEN a = a + 9

FOR b = 2 TO p

IF a MOD b <> 0 THEN EXIT FOR

NEXT

IF b = p + 1 THEN

PRINT a;

a = 0

EXIT DO

END IF

LOOP

LOOP