The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065515 Number of prime powers <= n. 22
 1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) > pi(n) = A000720(n). From Chayim Lowen, Aug 05 2015: (Start) a(n) <= pi(n) + A069623(n). Conjecture: a(n) >= pi(A069623(n)) + pi(n) + 1. Each term m is repeated A057820(m) times. (End) REFERENCES F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, Chapter 4. LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Prime Power FORMULA Partial sums of A010055. - Reinhard Zumkeller, Nov 22 2009 a(n) = 1 + Sum_{k=1..log_2(n)} pi(floor(n^(1/k))). - Chayim Lowen, Aug 05 2015 a(n) = 1 + Sum_{k=2..n} floor(2*A001222(k)/(tau(k^2)-1)) where tau is A000005(n). - Anthony Browne, May 17 2016 EXAMPLE There are 9 prime powers <= 12: 1=2^0, 2, 3, 4=2^2, 5, 7, 8=2^3, 9=3^2 and 11, so a(12) = 9. MAPLE N:= 100: # to get a(1) to a(N) L:= Vector(N): L[1]:= 1: p:= 1: while p < N do   p:= nextprime(p);   for k from 1 to floor(log[p](N)) do     L[p^k] := 1;   od od: ListTools:-PartialSums(convert(L, list)); # Robert Israel, May 03 2015 MATHEMATICA a[n_] := 1 + Count[ Range[2, n], p_ /; Length[ FactorInteger[p]] == 1]; Table[a[n], {n, 1, 73}] (* Jean-François Alcover, Oct 12 2011 *) Accumulate[Table[If[Length[FactorInteger[n]]==1, 1, 0], {n, 80}]] (* Harvey P. Dale, Aug 06 2016 *) Accumulate[Table[If[PrimePowerQ[n], 1, 0], {n, 120}]]+1 (* Harvey P. Dale, Sep 29 2016 *) PROG (Haskell) a065515 n = length \$ takeWhile (<= n) a000961_list -- Reinhard Zumkeller, Apr 25 2011 (PARI) a(n)=n+=.5; 1+sum(k=1, log(n)\log(2), primepi(n^(1/k))) \\ Charles R Greathouse IV, Apr 26 2012 CROSSREFS Cf. A000040, A000961, A000720, A276781 (ordinal transform). A025528(n) = a(n) - 1. Cf. A139555. - Reinhard Zumkeller, Oct 27 2010 Sequence in context: A020892 A196165 A138366 * A070545 A254828 A091863 Adjacent sequences:  A065512 A065513 A065514 * A065516 A065517 A065518 KEYWORD nice,nonn AUTHOR Reinhard Zumkeller, Nov 27 2001 STATUS approved

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

Last modified April 10 15:47 EDT 2021. Contains 342845 sequences. (Running on oeis4.)