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

1,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000005, A033950, A046754.

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

Sequence in context: A100010 A319761 A045510 * A065665 A321350 A249634

Adjacent sequences: A226322 A226323 A226324 * A226326 A226327 A226328

Keyword

nonn

Author

Alex Ratushnyak, Jun 04 2013

Status

approved