A281531 a(n) is the least numerator k such that the proper fraction k/n needs three or more terms as an Egyptian fraction, or 0 if no such numerator exists.

0, 0, 0, 4, 0, 3, 7, 7, 8, 5, 11, 3, 6, 7, 7, 4, 13, 3, 13, 9, 5, 5, 17, 4, 6, 8, 12, 4, 14, 3, 7, 5, 8, 11, 17, 3, 6, 9, 17, 4, 18, 3, 7, 11, 7, 5, 21, 3, 8, 7, 11, 4, 13, 9, 13, 7, 7, 7, 28, 3, 5, 13, 7, 4, 10, 3, 11, 11, 13, 5, 23, 3, 6, 11, 9, 5, 11, 3, 19

Offset

2,4

Comments

If n > 3 is prime, a(n) = A007978(n+1). - Robert Israel, Dec 26 2019

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Index entries for sequences related to Egyptian fractions

Maple

f:= proc(n) option remember; local k, T;
  T:= numtheory:-divisors(n^2);
  for k from 2 to n-1 do
    g:= igcd(k, n);
    if g > 1 then
       r:= procname(n/g);
       if k = r*g then return k fi;
    else
       if not member(-n mod k,  T mod k) then return k fi
    fi
  od;
0
end proc;
map(f, [$2..100]); # Robert Israel, Dec 25 2019

Mathematica

a[n_] := a[n] = Module[{k, T}, T = Divisors[n^2]; For[k = 2, k <= n - 1, k++, g = GCD[k, n]; If[g > 1, r = a[n/g]; If[k == r g, Return [k]], If[FreeQ[Mod[T, k], Mod[-n, k]], Return [k]]]]; 0];
a /@ Range[2, 100] (* Jean-François Alcover, Oct 06 2020, after Robert Israel *)

Prog

(Magma) lst:=[]; for n in [2..80] do for k in [1..n-1] do f:=k/n; x:=1; v:=0; if Numerator(f) eq 1 then v:=1; else while f lt 2/x do if Numerator(f-1/x) eq 1 then v:=1; break; end if; x+:=1; end while; end if; if v eq 0 then Append(~lst, k); break; end if; if k eq n-1 then Append(~lst, 0); end if; end for; end for; lst;

Crossrefs

Cf. A007978, A281530.

Sequence in context: A153615 A352718 A338736 * A248914 A246686 A048649

Adjacent sequences: A281528 A281529 A281530 * A281532 A281533 A281534

Keyword

nonn

Author

Arkadiusz Wesolowski, Jan 23 2017

Status

approved