|
Search: id:A056781
|
|
|
| A056781 |
|
Prime powers such that the 4th power of the number of divisors is not smaller than the number itself. |
|
+0
5
|
|
| 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 25, 27, 32, 49, 64, 81, 125, 128, 243, 256, 512, 625, 729, 1024, 2048, 2187, 4096, 6561, 8192, 16384, 32768, 65536
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
For any integers n, d[n]^4>n should form finite albeit very large sequence.
|
|
FORMULA
|
p^w<=(w+1)^4 i.e. p<=(w+1)^(4/w) restricts possible primes and their exponents
|
|
EXAMPLE
|
Equality holds in 12 cases: n=6561=3^8,d[n]=9 and d^4=9^4=3^8=n n=625,d[n]=5, so d^4=n
|
|
CROSSREFS
|
A000005, A034884, A035033-A035035.
Sequence in context: A115919 A038701 A127072 this_sequence A079446 A115975 A087797
Adjacent sequences: A056778 A056779 A056780 this_sequence A056782 A056783 A056784
|
|
KEYWORD
|
fini,full,nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Aug 18 2000
|
|
|
Search completed in 0.002 seconds
|
