A324981 a(n) = Product_{d|n} (d*pod(d)) where pod(k) = the product of the divisors of k (A007955).

1, 4, 9, 128, 25, 7776, 49, 65536, 2187, 100000, 121, 5159780352, 169, 537824, 759375, 1073741824, 289, 198359290368, 361, 512000000000, 4084101, 5153632, 529, 21035720123168587776, 78125, 11881376, 43046721, 10578455953408, 841, 15943230000000000000, 961

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Formula

a(n) = (Product_{d|n} d) * (Product_{d|n} pod(d)) = A007955(n) * A266265(n).

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

Example

a(6) = 1*pod(1) * 2*pod(2) * 3*pod(3) * 6*pod(6) = (1*1) * (2*2) * (3*3) * (6*36) = 7776.

Mathematica

Array[Times @@ Map[# Apply[Times, Divisors@ #] &, Divisors@ #] &, 31] (* Michael De Vlieger, Mar 24 2019 *)

Prog

(Magma) [&*[d * &*[c: c in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = my(d=divisors(n), p=1); fordiv(n, d, p*=d*vecprod(divisors(d))); p;  \\ Michel Marcus, Mar 22 2019

Crossrefs

Cf. A007955, A174933 (Sum_{d|n} (d*pod(d))), A266265.

Sequence in context: A063783 A168138 A267898 * A128524 A027451 A227744

Adjacent sequences: A324978 A324979 A324980 * A324982 A324983 A324984

Keyword

nonn

Author

Jaroslav Krizek, Mar 22 2019

Status

approved