The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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