

A283105


Numbers that are an integer multiple of the mean of their smallest and largest nontrivial divisors.


1



4, 9, 12, 25, 45, 49, 121, 169, 289, 361, 529, 637, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 13357, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569, 27889, 29929, 32041, 32761, 36481, 37249, 38809, 39601, 44521
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OFFSET

1,1


COMMENTS

No prime is in the sequence since there are no nontrivial divisors of a prime.
The sequence includes every number that is the square of a prime.
It is easy to show that the other terms are of the form (2p1)*p^2 where p and 2p1 are prime. Therefore, the mean of the two divisors in question is always an integer.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..600


EXAMPLE

4 is in the sequence because its smallest nontrivial divisor is 2, its largest nontrivial divisor is 2, and their mean is 2.
45 is in the sequence because its smallest nontrivial divisor is 3, its largest nontrivial divisor is 15, and their mean is 9, a divisor of 45.
10 is not in the sequence because it is not an integral multiple of 7/2, the mean of 2 and 5.


MATHEMATICA

mslndQ[n_]:=Module[{d=Divisors[n]}, Divisible[n, Mean[{d[[2]], d[[2]]}]]]; Select[Range[2, 50000], mslndQ] (* Harvey P. Dale, Jul 24 2017 *)


PROG

(PARI) is(n) = my(d=divisors(n), m=(d[2]+d[#d1])/2); if(n%m==0, 1, 0) \\ Felix Fröhlich, Feb 28 2017


CROSSREFS

Cf. A005382, A088595.
Sequence in context: A297414 A076794 A254520 * A179808 A083351 A055381
Adjacent sequences: A283102 A283103 A283104 * A283106 A283107 A283108


KEYWORD

nonn


AUTHOR

Emmanuel Vantieghem, Feb 28 2017


STATUS

approved



