A203967 The number of positive integers <= n that have a prime number of divisors.

0, 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = a(n-1) + A010055(n) * A010051(A100995(n)+1). - Reinhard Zumkeller, Jun 06 2013

Mathematica

Table[Total[Table[PrimePi[m^(1/n)], {n, Table[Prime[n]-1, {n, 1, 20}]}]], {m, 1, 100}]
tot = 0; Table[If[PrimeQ[DivisorSigma[0, n]], tot++]; tot, {n, 100}] (* T. D. Noe, Jan 10 2012 *)

Prog

(Haskell)
a203967 n = length $ takeWhile (<= n) a009087_list
-- Reinhard Zumkeller, Jun 06 2013

Crossrefs

Cf. A009087.

Sequence in context: A047784 A047742 A302778 * A365398 A365399 A267530

Adjacent sequences: A203964 A203965 A203966 * A203968 A203969 A203970

Keyword

nonn

Author

Geoffrey Critzer, Jan 08 2012

Status

approved