A332047 Numbers that are not distended, but all sums of subsets of divisors are distinct.

175, 442, 575, 638, 782, 806, 874, 875, 986, 1178, 1209, 1334, 1394, 1426, 1462, 1479, 1573, 1598, 1615, 1634, 1702, 1767, 1786, 1833, 1886, 2001, 2014, 2091, 2125, 2146, 2193, 2255, 2261, 2294, 2303, 2378, 2387, 2431, 2438, 2451, 2542, 2553, 2585, 2597, 2666, 2679, 2714, 2717, 2726, 2755, 2806

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..4100

Mathematics StackExchange, Are the "distended" numbers precisely the numbers for which no two subsets of their divisors have the same sum?

Example

a(3) = 575 has divisors 1, 5, 23, 25, 115, 575.  It is not distended because 1+5+23 >= 25, but the sums of all 2^6 subsets of divisors are distinct, so 575 is in the sequence.

Maple

filter:= proc(n) local d, sd, S, T, v;
  d:= sort(convert(numtheory:-divisors(n), list));
  sd:= ListTools:-PartialSums(d);
  if min(d[2..-1]-sd[1..-2])> 0 then return false fi;
  S:= {};
  T:= combinat:-subsets(d);
  while not T[finished] do
    v:= convert(T[nextvalue](), `+`);
    if member(v, S) then return false fi;
    S:= S union {v};
  od;
  true
end proc:
select(filter, [$1..3000]);

Crossrefs

Cf A051772.

Sequence in context: A015806 A369954 A109836 * A186211 A205748 A352109

Adjacent sequences: A332044 A332045 A332046 * A332048 A332049 A332050

Keyword

nonn

Author

Robert Israel, Feb 06 2020

Status

approved