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

1,3

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

Links

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

Example

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

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

Prog

(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

Crossrefs

Cf. A081515, A081516.

Sequence in context: A300792 A132082 A129644 * A374577 A104778 A356184

Adjacent sequences: A081514 A081515 A081516 * A081518 A081519 A081520

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 27 2003

Extensions

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

More terms from Jinyuan Wang, May 23 2020

Status

approved