A081517 Consider the smallest number m which can be expressed as the sum of n distinct numbers coprime to m. Sequence gives triangle (read by rows) of the set of coprime numbers pertaining to m. When there is a choice, use the lexicographically earliest solution.

1, 1, 2, 1, 2, 4, 1, 2, 3, 5, 1, 2, 3, 4, 7, 1, 2, 3, 4, 5, 8, 1, 2, 3, 4, 5, 6, 8, 1, 2, 3, 4, 5, 6, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19

Offset: 1

Author

Amarnath Murthy, Mar 27 2003

Keywords

• nonn
• tabl

Comments

For n >= 2, it appears that m is the least prime >= n*(n+1)/2, and row n consists of

1,2,3,...,n-1 and m - n*(n-1)/2. Robert Israel, Dec 22 2024

Examples

			Triangle begins:
1;
1,2;
1,2,4;
1,2,3,5;
1,2,3,4,7;
1,2,3,4,5,8;
		

Links

• Robert Israel, Table of n, a(n) for n = 1..7260 (first 120 rows, flattened)

Crossrefs

Cf. A081515, A081516.

Programs

Maple

g:= proc(S,m,n) # lex-first sublist of sorted list S of size n with sum m, or FAIL
    option remember;
    local nS,i,v;
    nS:= nops(S);
    if nS < n or convert(S[1..n],`+`) > m or convert(S[-n .. -1],`+`) < m then return FAIL fi;
    if n = 0 then if m = 0 then return [] else return FAIL fi fi;
    for i from 1 to nS while S[i] <= m do
       v:= procname(S[i+1..-1],m-S[i],n-1);
       if v <> FAIL then return [S[i],op(v)] fi
    od;
    FAIL
end proc:
f:= proc(n) local m,v;
   for m from 1 do
     v:= g(select(t -> igcd(t,m) = 1, [$1..m]),m,n);
     if v <> FAIL then return op(v) fi
   od
end proc:
for n from 1 to 20 do f(n) od; # Robert Israel, Dec 22 2024

PARI

row(n) = {my(m=n*(n-1)/2, v); for(k=m+n, oo, v=List([1]); for(i=2, k-m, if(gcd(k, i)==1, listput(v, i))); if(#v>=n, forsubset([#v, n], w, if(sum(i=1, n, v[w[i]])==k, return(vector(n, i, v[w[i]])))))); } \\ Jinyuan Wang, May 23 2020

Extensions

More terms from R. J. Mathar, Mar 23 2007

More terms from Jinyuan Wang, May 23 2020