A324980 a(n) = Product_{d|n} (d*sigma(d)) where sigma(k) = the sum of the divisors of k (A000203).

1, 6, 12, 168, 30, 5184, 56, 20160, 1404, 32400, 132, 48771072, 182, 112896, 129600, 9999360, 306, 425782656, 380, 762048000, 451584, 627264, 552, 8427641241600, 23250, 1192464, 1516320, 4956585984, 870, 21767823360000, 992, 20158709760, 2509056, 3370896

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = (Product_{d|n} d) * (Product_{d|n} sigma(d)) = A007955(n) * A206032(n).

a(p) = p*(p+1) for p = primes (A000040).

Example

a(6) = 1*sigma(1) * 2*sigma(2) * 3*sigma(3) * 6*sigma(6) = (1*1) * (2*3) * (3*4) * (6*12) = 5184.

Mathematica

Array[Times @@ Map[# DivisorSigma[1, #] &, Divisors@ #] &, 34] (* Michael De Vlieger, Mar 24 2019 *)

Prog

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

Crossrefs

Cf. A000203, A001001 (Sum_{d|n} (d*sigma(d))), A206032.

Sequence in context: A334985 A336723 A334805 * A014402 A181493 A360524

Adjacent sequences: A324977 A324978 A324979 * A324981 A324982 A324983

Keyword

nonn

Author

Jaroslav Krizek, Mar 22 2019

Status

approved