

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
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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



