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A267574
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Number of nontrivial prime powers p^k (k>1) less than 10^n.
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4
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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a[n_] := Sum[PrimePi [10^(n/k)], {k, 2, n * Log2[10]}]; Array[a, 20] (* Giovanni Resta, Apr 09 2016 *)
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PROG
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(SageMath)
gen = (p for p in srange(2, 10^n) if p.is_prime_power() and not p.is_prime())
return sum(1 for _ in gen)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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