|
|
A325030
|
|
a(n) = Product_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).
|
|
1
|
|
|
1, 6, 12, 336, 30, 31104, 56, 322560, 4212, 324000, 132, 84276412416, 182, 1580544, 1944000, 10239344640, 306, 2483164449792, 380, 6096384000000, 9483264, 13799808, 552, 1610547321930095001600, 116250, 31004064, 122821920, 108806975520768, 870
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
n divides a(n) for all n.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Product_{d|n} sigma(d) * Product_{d|n} pod(d) = A206032(n) * A266265(n).
a(p) = p*(p+1) for p = primes (A000040).
|
|
EXAMPLE
|
a(6) = (sigma(1)*pod(1)) * (sigma(2)*pod(2)) * (sigma(3)*pod(3)) * (sigma(6)*pod(6)) = (1*1) * (3*2) * (4*3) * (12*36) = 31104.
|
|
PROG
|
(Magma) [&*[&+ [c: c in Divisors(d)] * &*[c: c in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, my(dd=divisors(d[k])); vecsum(dd)*vecprod(dd)); \\ Michel Marcus, Apr 25 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|