A332047 - OEIS

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

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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;