A062509 a(n) = n^omega(n).

1, 2, 3, 4, 5, 36, 7, 8, 9, 100, 11, 144, 13, 196, 225, 16, 17, 324, 19, 400, 441, 484, 23, 576, 25, 676, 27, 784, 29, 27000, 31, 32, 1089, 1156, 1225, 1296, 37, 1444, 1521, 1600, 41, 74088, 43, 1936, 2025, 2116, 47, 2304, 49, 2500, 2601, 2704, 53, 2916

Offset

1,2

Comments

Not always equal to product of unitary divisors of n [compare with A061537]. This deviates from A061537 at 30, 42, 60, 66, etc.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{d|n} tau(d^n)*mu(n/d). - Ridouane Oudra, Sep 17 2022

Example

n=30: a(30) = 30^3 = 27000;
n=72: a(72) = 72^2 = 5184.

Mathematica

Table[n^PrimeNu[n], {n, 60}] (* Harvey P. Dale, Jan 14 2013 *)

Prog

(PARI) a(n)={n^omega(n)} \\ Harry J. Smith, Aug 08 2009
(Haskell)
a062509 n = n ^ a001221 n  -- Reinhard Zumkeller, Sep 13 2013

Crossrefs

Cf. A001221, A061537, A034444, A000005, A033992.

Cf. A176029, A229109.

Sequence in context: A124128 A286902 A037401 * A061537 A306329 A274029

Adjacent sequences: A062506 A062507 A062508 * A062510 A062511 A062512

Keyword

nonn

Author

Labos Elemer, Jul 13 2001

Status

approved