login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089580 Total number of perfect powers > 1 below 10^n, counting multiple representations separately. 6
3, 15, 49, 143, 406, 1174, 3507, 10674, 32965, 102716, 321797, 1011533, 3186389, 10050743, 31730134, 100228040, 316713623, 1001037546, 3164497349, 10004755374, 31632975598, 100021893194, 316274794666, 1000101078148, 3162495003352, 10000467510247, 31623782520064, 100002164895587 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Robert G. Wilson v, Jul 17 2016: (Start)
a(n) ~ sqrt(10^n).
a(n) - A089579(n) = A275358(n).
The four terms which make up the difference a(2) - A089579(2) are: 16 = 2^4 = 4^2, 64 = 2^6 = 4^3 = 8^2 and 81 = 3^4 = 9^2; one for 16, two for 64 and one for 81 making a total of 4. See A117453.
(End)
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..1998 (n = 1..100 from Robert G. Wilson, n = 101..400 from Karl-Heinz Hofmann)
Karl-Heinz Hofmann, Python program.
FORMULA
a(n) = Sum_{k = 1..n} A060298(k). - Karl-Heinz Hofmann, Sep 18 2023
EXAMPLE
16 = 2^4 = 4^2 counts double, 256 = 2^8 = 4^4 = 16^2 counts three times.
MATHEMATICA
Table[lim=10^n-1; Sum[Floor[lim^(1/k)]-1, {k, 2, Floor[Log[2, lim]]}], {n, 30}] (* T. D. Noe, Nov 16 2006 *)
PROG
(Python) # see link.
CROSSREFS
Cf. A089579 (counting multiple representations only once).
Sequence in context: A316853 A061316 A124161 * A034564 A012203 A112586
KEYWORD
nonn
AUTHOR
Martin Renner, Dec 29 2003
EXTENSIONS
2 more terms from Martin Renner, Oct 02 2004
More terms from T. D. Noe, Nov 16 2006
More precise name by Hugo Pfoertner, Sep 16 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 07:21 EDT 2024. Contains 370955 sequences. (Running on oeis4.)