A236858 Irregular table where row n contains numbers from 1 to the least common multiple (LCM) of {1, 2, ..., n}. Row 0 is given as a(0)=1.

1, 1, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60

Offset

0,4

Comments

Numbers 1..A003418(n) followed by numbers 1..A003418(n+1), etc., where A003418(n) gives the least common multiple (LCM) of {1, 2, ..., n} for n >= 1 and A003418(0)=1.

Useful when computing irregular tables like A238280. Note that as A238280 begins with row 1, it starts referring to this sequence only from a(1) onward.

Links

Antti Karttunen, Rows 0..10 of the table, flattened

Formula

a(n) = n - A236856(A236857(n)- 1).

Example

The sequence can be viewed also as an irregular table that starts as:
0 | 1;
1 | 1;
2 | 1, 2;
3 | 1, 2, 3, 4, 5, 6;
4 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
...

Mathematica

Join[{1}, Table[Range[LCM@@Range[n]], {n, 6}]//Flatten] (* Harvey P. Dale, Apr 29 2019 *)

Prog

(Scheme) (define (A236858 n) (- n (A236856 (- (A236857 n) 1))))

Crossrefs

A003418(n) gives the last term of each row n.

Cf. A220661, A236856, A236857, A238280.

Sequence in context: A309932 A363968 A058886 * A220661 A369900 A137846

Adjacent sequences: A236855 A236856 A236857 * A236859 A236860 A236861

Keyword

nonn,tabf,easy

Author

Antti Karttunen, Feb 27 2014

Status

approved