OFFSET
1,3
COMMENTS
This sequence is the generalization of the problem A1737 proposed on French mathematical site Diophante (see link).
a(2) = 0 but all other terms are nonzero.
LINKS
Diophante, A1737 - Fidèles au rendez-vous (in French).
EXAMPLE
In the following triangle, the n-th row gives an example of a set of n divisors d_1, ..., d_n of a(n) such that a(n) = d_1 + ... + d_n = lcm(d_1, ..., d_n):
.
n m d_1 d_2 d_3 d_4 d_5 d_6 d_7 d_8 d_9 d10 d11 d12
-----------------------------------------------------------
1 1 1
2 0
3 6 1 2 3
4 18 1 2 6 9
5 28 1 2 4 7 14
6 24 1 2 3 4 6 8
7 48 1 2 3 4 8 16 24
8 60 1 2 3 4 5 10 15 20
9 84 1 2 3 4 6 7 12 21 28
10 120 1 2 3 4 5 6 15 20 24 40
11 120 1 2 3 4 5 6 8 12 15 24 40
12 120 1 2 3 4 5 6 8 10 12 15 24 30
However, for a given value of a(n) = m, there may be more than one way to choose d_1, ..., d_n. For example, for n=10, a(10)=120 and all seventeen solutions provided by Jinyuan Wang in the Comments section of A081512 are also solutions here.
PROG
(PARI) isok(m, n) = {my(d=divisors(m)); if (#d<n, return(0)); forsubset([#d, n], s, my(vd = vector(n, k, d[s[k]])); if (lcm(vd) == vecsum(vd), return(1)); ); }
a(n) = {if (n==1, return(1)); if (n==2, return(0)); my(m=1); while (!isok(m, n), m++); m; } \\ Michel Marcus, Jun 25 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jun 25 2022
EXTENSIONS
More terms from Jinyuan Wang, Jun 25 2022
STATUS
approved