

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.).


1



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
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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: A108587 A079424 A270383 * A057826 A268657 A232742
Adjacent sequences: A088342 A088343 A088344 * A088346 A088347 A088348


KEYWORD

nonn


AUTHOR

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


STATUS

approved



