A325938 a(n) = omega(n)^tau(n), where omega=A001221 and tau=A000005.

0, 1, 1, 1, 1, 16, 1, 1, 1, 16, 1, 64, 1, 16, 16, 1, 1, 64, 1, 64, 16, 16, 1, 256, 1, 16, 1, 64, 1, 6561, 1, 1, 16, 16, 16, 512, 1, 16, 16, 256, 1, 6561, 1, 64, 64, 16, 1, 1024, 1, 64, 16, 64, 1, 256, 16, 256, 16, 16, 1, 531441, 1, 16, 64, 1, 16, 6561, 1, 64

Offset

1,6

Links

Hauke Löffler, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001221(n) ^ A000005(n).

Example

a(5) = 1; 5 has one distinct prime divisor {5} and two divisors {1,5}, so a(5) = 1^2 = 1.
a(6) = 16; 6 has two distinct prime divisors {2,3} and four divisors {1,2,3,6}, so a(6) = 2^4 = 16.

Prog

(SageMath)
[ len(prime_divisors(x))^(len(divisors(x))) for x in range(1, 20) ]
(PARI) a(n) = {omega(n)^numdiv(n)} \\ Andrew Howroyd, Sep 09 2019

Crossrefs

Cf. A000005(tau), A001221(omega), A110088, A248577.

Sequence in context: A040259 A353806 A040260 * A361132 A040258 A040257

Adjacent sequences: A325935 A325936 A325937 * A325939 A325940 A325941

Keyword

nonn

Author

Hauke Löffler, Sep 09 2019

Status

approved