A081514 - OEIS

%I #25 Oct 24 2024 09:24:32

%S 1,0,0,1,2,3,1,2,3,6,1,2,3,6,12,1,2,3,4,6,8,1,2,3,4,6,8,24,1,2,3,4,5,

%T 10,15,20,1,2,3,4,6,7,12,21,28,1,2,3,4,5,6,15,20,24,40,1,2,3,4,5,6,8,

%U 12,15,24,40,1,2,3,4,5,6,8,10,12,15,24,30,1,2,3,4,5,6,9,10,12,18,20,30,60

%N Triangle read by rows: row n = lexicographically earliest choice for n distinct divisors of A081512(n) = m whose sum is m.

%C A081512(n) = smallest number m which can be expressed as the sum of n of its distinct divisors, or 0 if no such number exists. (n=2 is the only time A081512(n) = 0.)

%C Look at all sets of n distinct divisors d_1, ..., d_n of m = A081512(n) such that d_1+...+d_n = m, and choose the lexicographically earliest solution.  That is row n of the current triangle.

%C The value of d_n in the lexicographically earliest solution is given in A081513.

%H David A. Corneth, <a href="/A081514/b081514.txt">Table of n, a(n) for n = 1..10296</a>

%e The lexicographically earliest solutions are:

%e [1]

%e [0, 0]

%e [1, 2, 3]

%e [1, 2, 3, 6]

%e [1, 2, 3, 6, 12]

%e [1, 2, 3, 4, 6, 8]

%e [1, 2, 3, 4, 6, 8, 24]

%e [1, 2, 3, 4, 5, 10, 15, 20]

%e [1, 2, 3, 4, 6, 7, 12, 21, 28]

%e [1, 2, 3, 4, 5, 6, 15, 20, 24, 40]

%e [1, 2, 3, 4, 5, 6, 8, 12, 15, 24, 40]

%e [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30]

%e [1, 2, 3, 4, 5, 6, 9, 10, 12, 18, 20, 30, 60]

%e ...

%Y Cf. A081512, A081513.

%K nonn,tabl

%O 1,5

%A _Amarnath Murthy_, Mar 27 2003

%E Corrected by Caleb M. Shor (cshor(AT)bates.edu), Sep 26 2007

%E Edited by _N. J. A. Sloane_, May 24 2020 at the suggestion of _Jinyuan Wang_, who also gave the first 13 rows.