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A089579 Total number of exact powers below 10^n (without counting duplicates). 5
3, 11, 39, 123, 365, 1109, 3393, 10489, 32668, 102229, 320988, 1010194, 3184136, 10046919, 31723590, 100216743, 316694003, 1001003330, 3164437423, 10004650116, 31632790242, 100021566155, 316274216760, 1000100055682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Robert G. Wilson v, Jul 17 2016: (Start)

Lim {n->inf.} a(n) = sqrt(10^n).

The difference between A089580(n)-a(n) = 0, 4, 10, 20, 41, 65, 114, 185, 297, 487, 809, 1339, 2253, 3824, 6544, 11297, 19620, 34216, 59926, 105258, 185356, 327039, 577906, 1022466, ...

The four terms which make up the difference between A089580(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

Robert G. Wilson v, Table of n, a(n) for n = 1..100

EXAMPLE

For n=2, the 11 perfect powers below 10^2 = 100 are: 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81. - Michael B. Porter, Jul 18 2016

MATHEMATICA

Table[lim=10^n-1; Sum[ -(Floor[lim^(1/k)]-1)*MoebiusMu[k], {k, 2, Floor[Log[2, lim]]}], {n, 30}] (* T. D. Noe, Nov 16 2006 *)

CROSSREFS

Cf. A001597, A089580.

Sequence in context: A192528 A112674 A064086 * A227638 A166336 A002783

Adjacent sequences:  A089576 A089577 A089578 * A089580 A089581 A089582

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

STATUS

approved

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)