A338576 a(n) = n * pod(n) where pod(n) = the product of divisors of n (A007955).

1, 4, 9, 32, 25, 216, 49, 512, 243, 1000, 121, 20736, 169, 2744, 3375, 16384, 289, 104976, 361, 160000, 9261, 10648, 529, 7962624, 3125, 17576, 19683, 614656, 841, 24300000, 961, 1048576, 35937, 39304, 42875, 362797056, 1369, 54872, 59319, 102400000, 1681

Offset

1,2

Links

Table of n, a(n) for n=1..41.

Formula

a(n) = n * A007955(n) = n^2 * A007956(n).

a(n) = lcm(n, pod(n)) * gcd(n, pod(n)).

a(p) = p^2 for p = primes (A000040).

Example

a(6) = 6 * pod(6) = 6 * 36 = 216.

Mathematica

a[n_] := n^(1 + DivisorSigma[0, n]/2); Array[a, 50] (* Amiram Eldar, Nov 03 2020 *)

Prog

(Magma) [n * &*Divisors(n): n in [1..100]]
(PARI) a(n) = n*vecprod(divisors(n)); \\ Michel Marcus, Nov 03 2020
(Python)
from math import isqrt
from sympy import divisor_count
def A338576(n): return (isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2+1) # Chai Wah Wu, Jun 25 2022

Crossrefs

Cf. A007955 (pod(n)), A007956 (pod(n) / n).

Similar sequences: A038040 (n * tau(n)), A064987 (n * sigma(n)).

Cf. A174935 (partial sums of a(n)).

Sequence in context: A361987 A071378 A053192 * A270618 A270634 A324020

Adjacent sequences: A338573 A338574 A338575 * A338577 A338578 A338579

Keyword

nonn

Author

Jaroslav Krizek, Nov 03 2020

Status

approved