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
KEYWORD
nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 07 2003
STATUS
approved