login
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).
3
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
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
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