

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 nth 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
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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 n2 members of row n > 2 are {1, 2, ..., n2}. If the maximal prime powers dividing A081535(n) are all less than n, the ending terms are {n1, A081535(n)n*(n1)/2}. Otherwise, they are {a, b} where either a or b is the largest prime power dividing A081535(n) and a + b = A081535(n)  (n1)*(n2)/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: A249111 A166871 A275728 * 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



