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A267574 Number of nontrivial prime powers p^k (k>1) less than 10^n. 2
3, 10, 25, 51, 108, 236, 555, 1404, 3689, 10084, 28156, 80070, 230567, 670121, 1962689, 5782467, 17124205, 50930439, 152043591, 455389239, 1367883343, 4119448336, 12434731101, 37613760489, 113995567274, 346090346046, 1052421430208, 3205047877403, 9774085385959, 29845027519170, 91239740502962, 279240320955782, 855506687516860, 2623565774949376 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Computed up to 10^19 by program. The program was written in C, and is rather long. It starts by finding all prime numbers up to 4*10^9, then uses that to count all powers of these primes up to 10^19.

LINKS

Table of n, a(n) for n=1..34.

Daniel Mondot, Math puzzle about Least Common Multiple (french:PPCM)

EXAMPLE

For n=1, there are 3 powers of prime numbers less than 10^1: 2^2, 2^3 and 3^2. i.e. 4, 8, 9.

For n=2, there are 10 powers of prime numbers less than 10^2: 4, 8, 9, 16, 25, 27, 32, 49, 64, 81.

MATHEMATICA

a[n_] := Sum[PrimePi [10^(n/k)], {k, 2, n * Log2[10]}]; Array[a, 20] (* Giovanni Resta, Apr 09 2016 *)

CROSSREFS

Cf. A246547, A006880.

Sequence in context: A176952 A212068 A162607 * A047667 A192963 A000247

Adjacent sequences:  A267571 A267572 A267573 * A267575 A267576 A267577

KEYWORD

nonn

AUTHOR

Daniel Mondot, Jan 17 2016

EXTENSIONS

a(20)-a(26) from Chai Wah Wu, Jan 25 2016

a(27)-a(34) from Giovanni Resta, Apr 09 2016

STATUS

approved

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Last modified July 2 16:47 EDT 2020. Contains 335404 sequences. (Running on oeis4.)