|
|
A108640
|
|
a(n) = Product_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = sum{j|k} j^m.
|
|
1
|
|
|
1, 2, 6, 60, 1260, 239904, 123263712, 872883648000, 35330106763980000, 15502816844111220549120, 32196148399600498119169883520, 2560463149313858442381787649990400000, 717635502576022020068175045395317927056000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
EXAMPLE
|
a(5) = 1^4 * (1^3 +2^3) * (1^2 +3^2) * (1^1 +2^1 +4^1) * (1^0 +5^0) = 1 * 9 * 10 * 7 * 2 = 1260.
|
|
MAPLE
|
with(numtheory): s:=proc(n, k) local div: div:=divisors(n): sum(div[j]^k, j=1..tau(n)) end: a:=n->product(s(i, n-i), i=1..n): seq(a(n), n=1..14); # Emeric Deutsch, Jul 13 2005
|
|
MATHEMATICA
|
Table[Product[DivisorSigma[j, n-j], {j, 0, n-1}], {n, 30}] (* G. C. Greubel, Oct 18 2023 *)
|
|
PROG
|
(PARI) a(n) = prod(k=1, n, sigma(k, n-k)); \\ Michel Marcus, Aug 16 2019
(Magma)
A108639:= func< n | (&*[DivisorSigma(j, n-j): j in [0..n-1]]) >;
(SageMath)
def A108640(n): return product(sigma(n-j, j) for j in range(n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|