|
Search: id:A013969
|
|
|
| A013969 |
|
sigma_21(n), the sum of the 21st powers of the divisors of n. |
|
+0
3
|
|
| 1, 2097153, 10460353204, 4398048608257, 476837158203126, 21936961102828212, 558545864083284008, 9223376434903384065, 109418989141972712413, 1000000476837160300278, 7400249944258160101212, 46005141850728850805428
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.
|
|
FORMULA
|
G.f. sum(k>=1, k^21*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
|
|
CROSSREFS
|
Adjacent sequences: A013966 A013967 A013968 this_sequence A013970 A013971 A013972
Sequence in context: A017706 A010809 A017705 this_sequence A036099 A043630 A138084
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
