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A304520
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a(n) is the number of n-digit prime powers.
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0
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7, 28, 158, 1087, 8420, 69034, 586400, 5097725, 45088364, 404211372, 3663020374, 33489909119, 308457775318, 2858876653517, 26639629964435, 249393774431034, 2344318827962046, 22116397163892861, 209317713089716899, 1986761935587919881, 18906449884370307192
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OFFSET
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1,1
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COMMENTS
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"Prime powers" here are defined as in A246655, so 1 is not counted here as a prime power.
For the number of n-digit primes, see A006879.
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LINKS
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EXAMPLE
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a(1) = 7 because there are 7 1-digit numbers that are prime powers: 2=2^1, 3=3^1, 4=2^2, 5=5^1, 7=7^1, 8=2^3, and 9=3^2.
a(2) = 28 because there are 28 2-digit prime powers: the 21 2-digit primes (11, 13, ..., 97), 2 squares of primes (25=5^2 and 49=7^2), 1 cube of a prime (27=3^3), 2 fourth powers of primes (16=2^4 and 81=3^4), 1 fifth power of a prime (32=2^5), and 1 sixth power of a prime (64=2^6).
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MATHEMATICA
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PROG
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(Magma) /* gives first 9 terms */ a:=[]; for n in [1..9] do tMin:=10^(n-1); tMax:=10^n-1; c:=0; for k in [1..Floor(Log(2, tMax))] do pMin:=Ceiling(tMin^(1/k)); pMax:=Floor(tMax^(1/k)); if pMin le pMax then c+:=#PrimesInInterval(pMin, pMax); end if; end for; a[n]:=c; end for; a;
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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