A081536 Let f(n) be smallest number k which is a sum of n distinct numbers whose LCM is a multiple of k. Sequence gives triangle read by rows in which n-th row consists of those n numbers (row 2 is 0, 0 by convention).

1, 0, 0, 1, 2, 3, 1, 2, 4, 7, 1, 2, 3, 4, 5, 1, 2, 3, 4, 6, 8, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 8, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

Offset

1,5

Comments

Row 2k+1 consists of the first 2k+1 numbers, and row 2k consists of the first 2k numbers iff 2k+1 is not a power of a prime. - Charlie Neder, Feb 03 2019

Links

Table of n, a(n) for n=1..91.

Formula

The first n-2 members of row n > 2 are {1, 2, ..., n-2}. If the maximal prime powers dividing A081535(n) are all less than n, the ending terms are {n-1, A081535(n)-n*(n-1)/2}. Otherwise, they are {a, b} where either a or b is the largest prime power dividing A081535(n) and a + b = A081535(n) - (n-1)*(n-2)/2. - Charlie Neder, Feb 03 2019

Example

Triangle begins:
  1;
  0, 0;
  1, 2, 3; (1+2+3 = 6 | 6 = lcm(1,2,3))
  1, 2, 4, 7; (1+2+4+7 = 14 | 28 = lcm(1,2,4,7))
  1, 2, 3, 4, 5;
  ...

Crossrefs

Cf. A081535, A081537, A081538.

Sequence in context: A360476 A275728 A364057 * A297497 A152736 A139246

Adjacent sequences: A081533 A081534 A081535 * A081537 A081538 A081539

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 28 2003

Extensions

Corrected and extended by Charlie Neder, Feb 03 2019

More terms from Jinyuan Wang, May 03 2020

Status

approved