A226325 Integers of the form n/tau(n)^2 as n runs through the integers, where tau(n) is the number of divisors of n.

1, 1, 2, 25, 3, 2, 5, 9, 25, 81, 6, 4, 16, 3, 5, 28, 36, 12, 128, 81, 81, 24, 7, 40, 8, 21, 28, 50, 12, 11, 16, 12, 96, 49, 13, 35, 44, 2401, 52, 45, 17, 36, 19, 160, 225, 68, 63, 23, 76, 30, 28, 36, 72, 21, 224, 92, 29, 77, 121, 31, 18, 27, 30, 91, 99, 116, 128, 37, 124

Offset: 1

Author

Alex Ratushnyak, Jun 04 2013

Keywords

• nonn

Examples

			A046754(3) = 128, A000005(128) = 8, so a(3) = 128 / 8^2 = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A033950, A046754.

Cf. A036762 (if d(n) divides n, then n/d(n) is appended to the sequence).

Programs

Maple

for n from 1 to 1000000 do
    r := n/(numtheory[tau](n))^2 ;
    if type(r,'integer') then
        printf("%d,",r);
    end if;
end do: # R. J. Mathar, Jun 07 2013

Mathematica

Select[Table[n/DivisorSigma[0,n]^2,{n,10^6}],IntegerQ] (* Harvey P. Dale, Jan 01 2015 *)

Formula

a(n) = A046754(n) / A000005(A046754(n))^2.