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.).

6, 12, 18, 28, 45, 48, 56, 72, 80, 96, 117, 196, 396, 475, 496, 702, 704, 775, 992, 1100, 1326, 1568, 1792, 2009, 2150, 2622, 2952, 3042, 3321, 3672, 4140, 5328, 5852, 6750, 6860, 7154, 7605, 7680, 8128, 9102, 10575, 11008, 12126, 12168, 12384, 12810

Offset: 1

Author

Chuck Seggelin, Nov 07 2003

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070039.

Programs

Maple

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 f1 then if i mod v = 0 then print(i,v,i/v); j := j union {i} fi; fi; fi; od; j;

Mathematica

ds[n_] := DivisorSum[n, # &, # < Sqrt[n] &]; aQ[n_] := (d = ds[n]) > 1 && Divisible[n, d]; Select[Range[12810], aQ] (* Amiram Eldar, Aug 28 2019 *)