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A304520 a(n) is the number of n-digit prime powers. 1
7, 28, 158, 1087, 8420, 69034, 586400, 5097725, 45088364, 404211372, 3663020374, 33489909119, 308457775318, 2858876653517, 26639629964435, 249393774431034, 2344318827962046, 22116397163892861, 209317713089716899, 1986761935587919881, 18906449884370307192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"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.

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

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).

MATHEMATICA

Prepend[Differences@ #, First@ #] &@ Array[Sum[PrimePi[10^(#/k)], {k, # Log2@ 10}] &, 12] (* Michael De Vlieger, May 20 2018, after Robert G. Wilson v at A267712 *)

PROG

(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;

CROSSREFS

Cf. A006879, A246655, A267712 (partial sums).

Sequence in context: A025030 A001554 A026664 * A335759 A224663 A203296

Adjacent sequences:  A304517 A304518 A304519 * A304521 A304522 A304523

KEYWORD

nonn,base

AUTHOR

Jon E. Schoenfield, May 13 2018

STATUS

approved

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Last modified October 3 02:59 EDT 2022. Contains 357230 sequences. (Running on oeis4.)