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A088345 n is divisible by the sum of all divisors of n which are less than the square root of n (values of n where 1 is the only divisor less than sqrt(n) are excluded as trivial cases.).

%I A088345 #7 Jun 08 2025 16:15:42
%S A088345 6,12,18,28,45,48,56,72,80,96,117,196,396,475,496,702,704,775,992,
%T A088345 1100,1326,1568,1792,2009,2150,2622,2952,3042,3321,3672,4140,5328,
%U A088345 5852,6750,6860,7154,7605,7680,8128,9102,10575,11008,12126,12168,12384,12810
%N A088345 n is divisible by the sum of all divisors of n which are less than the square root of n (values of n where 1 is the only divisor less than sqrt(n) are excluded as trivial cases.).
%C A088345 If values of n where only the divisor 1 is < sqrt(n) were not excluded, then this sequence would include the primes and the squares of primes.
%H A088345 Amiram Eldar, <a href="/A088345/b088345.txt">Table of n, a(n) for n = 1..10000</a>
%e A088345 a(4)=28 because sqrt(28)=5.291502622 and the divisors of 28 which are less than 5.291502622 are 1, 2 and 4. These divisors sum to 7 which divides 28.
%p A088345 j := {}; for i to 1000 do; d := divisors(i) minus {i}; if d<>{1} then v := 0; s := evalf(sqrt(i)); for f in d do; if f<s then v := v+f; fi; od; if v>1 then if i mod v = 0 then print(i,v,i/v); j := j union {i} fi; fi; fi; od; j;
%t A088345 ds[n_] := DivisorSum[n, # &, # < Sqrt[n] &]; aQ[n_] := (d = ds[n]) > 1 && Divisible[n, d]; Select[Range[12810], aQ] (* _Amiram Eldar_, Aug 28 2019 *)
%Y A088345 Cf. A070039.
%K A088345 nonn
%O A088345 1,1
%A A088345 _Chuck Seggelin_, Nov 07 2003