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

1,1

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.

Links

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

Example

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.

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 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;

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 *)

Crossrefs

Cf. A070039.

Sequence in context: A079424 A350685 A270383 * A057826 A334543 A330853

Adjacent sequences: A088342 A088343 A088344 * A088346 A088347 A088348

Keyword

nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 07 2003

Status

approved