OFFSET
1,2
COMMENTS
Product_{d|n} (d/tau(d)) >= 1 for all n >= 1.
Corresponding values of integers h: 1, 1, 6, 36, 216, 7776, 43046721, 2916000000, 33177600000000, ...
From Robert Israel, Mar 24 2019: (Start)
All terms other than 1 and 2 are divisible by 12.
Contains 36*p^2 for all primes p >= 5, and 480*p for all primes p >= 7. In particular, the sequence is infinite. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
A324507(a(n)) = 1.
EXAMPLE
12 is a term because Product_{d|12} (d/tau(d)) = (1/tau(1)) * (2/tau(2)) * (3/tau(3)) * (4/tau(4)) * (6/tau(6)) * (12/tau(12)) = (1/1) * (2/2) * (3/2) * (4/3) * (6/4) * (12/6) = 6 (integer).
MAPLE
filter:= proc(n) uses numtheory; local d;
mul(d/tau(d), d=divisors(n))::integer;
end proc:
select(filter, [$1..20000]); # Robert Israel, Mar 24 2019
MATHEMATICA
Select[Range[15000], IntegerQ[Product[k/DivisorSigma[0, k], {k, Divisors[#]}]] &] (* G. C. Greubel, Mar 04 2019 *)
PROG
(Magma) [n: n in [1..1000] | IsIntegral(&*[d / #[c: c in Divisors(d)] : d in Divisors(n)])]
(Sage) [n for n in (1..15000) if (product(k/sigma(k, 0) for k in n.divisors())).is_integer()] # G. C. Greubel, Mar 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 03 2019
STATUS
approved