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A089580 Total number of exact powers below 10^n (counting duplicates). 5
3, 15, 49, 143, 406, 1174, 3507, 10674, 32965, 102716, 321797, 1011533, 3186389, 10050743, 31730134, 100228040, 316713623, 1001037546, 3164497349, 10004755374, 31632975598, 100021893194, 316274794666, 1000101078148 (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).

The difference between a(n) - A089579(n) = 0, 4, 10, 20, 41, 65, 114, 185, 297, 487, 809, 1339, 2253, 3824, 6544, 11297, 19620, 34216, 59926, 105258, 185356, 327039, ..., A275358.

The four terms which make up the difference between 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

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

EXAMPLE

E.g. 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 *)

CROSSREFS

Cf. A001597, A072103, A117453, A275358.

Cf. A089579 (not counting duplicates).

Sequence in context: A316853 A061316 A124161 * A034564 A012203 A112586

Adjacent sequences:  A089577 A089578 A089579 * A089581 A089582 A089583

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 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)