OFFSET
1,2
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Plot of a(n)/n^(3/2) for n = 1..20000
Eric Weisstein's World of Mathematics, Divisor Product.
Eric Weisstein's World of Mathematics, Divisor Function.
Wikipedia, Arithmetic number.
EXAMPLE
a(2) = 6 because 6 has 4 divisors {1,2,3,6}, 1*2*3*6/4 = 9, 1*2*3*6/(1 + 2 + 3 + 6) = 3 and (1 + 2 + 3 + 6)/4 = 3 are integer.
MAPLE
with(numtheory): P:=proc(q) local a, b, k, n; for n from 1 to q do
a:=divisors(n); b:=mul(a[k], k=1..nops(a));
if type(sigma(n)/tau(n), integer) and type(b/sigma(n), integer) and
type(b/tau(n), integer) then print(n); fi;
od; end: P(10^5); # Paolo P. Lava, Oct 20 2016
MATHEMATICA
Select[Range[4000], Divisible[Sqrt[#1]^DivisorSigma[0, #1], DivisorSigma[1, #1]] && Divisible[Sqrt[#1]^DivisorSigma[0, #1], DivisorSigma[0, #1]] && Divisible[DivisorSigma[1, #1], DivisorSigma[0, #1]] & ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 19 2016
STATUS
approved