A332047 - OEIS

%I #11 Feb 18 2021 00:26:05

%S 175,442,575,638,782,806,874,875,986,1178,1209,1334,1394,1426,1462,

%T 1479,1573,1598,1615,1634,1702,1767,1786,1833,1886,2001,2014,2091,

%U 2125,2146,2193,2255,2261,2294,2303,2378,2387,2431,2438,2451,2542,2553,2585,2597,2666,2679,2714,2717,2726,2755,2806

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

%H Robert Israel, <a href="/A332047/b332047.txt">Table of n, a(n) for n = 1..4100</a>

%H Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3536777/are-the-distended-numbers-precisely-the-numbers-for-which-no-two-subsets-of-th">Are the "distended" numbers precisely the numbers for which no two subsets of their divisors have the same sum?</a>

%e 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.

%p filter:= proc(n) local d, sd, S, T, v;

%p   d:= sort(convert(numtheory:-divisors(n),list));

%p   sd:= ListTools:-PartialSums(d);

%p   if min(d[2..-1]-sd[1..-2])> 0 then return false fi;

%p   S:= {};

%p   T:= combinat:-subsets(d);

%p   while not T[finished] do

%p     v:= convert(T[nextvalue](),`+`);

%p     if member(v,S) then return false fi;

%p     S:= S union {v};

%p   od;

%p   true

%p end proc:

%p select(filter, [$1..3000]);

%Y Cf A051772.

%K nonn

%O 1,1

%A _Robert Israel_, Feb 06 2020