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A076411 Number of perfect powers < n. 3
0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Perfect powers are in A001597. The function a(n) increases much more slowly than pi(n): e.g., a(1765)=54 and pi(1765)=274. See also A076412.

a(n) >= A000196(n-1). - Robert Israel, Jul 31 2015

This is essentially the same as A069623 which is the main entry, see there for more formulas. - M. F. Hasler, Aug 16 2015

LINKS

Table of n, a(n) for n=1..86.

FORMULA

a(n) = n^(1/2) + n^(1/3) + n^(1/5) - n^(1/6) + n^(1/7) - n^(1/10) + O(n^(1/11)). - Charles R Greathouse IV, Aug 14 2015

EXAMPLE

a(9)=3 because there are 3 perfect powers less than 9: 1,4,8.

PROG

(PARI) a(n)=n--; n-sum(k=1, logint(n, 2), moebius(k)*(sqrtnint(n, k)-1)) \\ Charles R Greathouse IV, Jul 21 2017

CROSSREFS

A069623(n) = a(n+1) is the main entry.

Cf. A001597, A076412, A075802, A096623.

Sequence in context: A234451 A085501 A069623 * A217038 A309196 A243283

Adjacent sequences:  A076408 A076409 A076410 * A076412 A076413 A076414

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 09 2002

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)