A390602 Number of numbers m <= 10^n that have a prime divisor greater than sqrt(10^n) (i.e., A006530(m)>sqrt(10^n)).

0, 3, 54, 566, 6284, 64181, 655701, 6637843, 66731910, 671100019, 6734525690, 67552542839, 677104572039, 6784024897767, 67951242054748, 680453355924467, 6812803534350769, 68200185604163133, 682641287397034215, 6832108697465736102, 68372127364480522871, 684182105083771305876

Offset

0,2

Links

Henri Lifchitz, Table of n, a(n) for n = 0..21

Formula

a(n) = Sum_{prime p > sqrt(10^n)} floor(10^n/p).

a(n) = Sum_{k <= sqrt(10^n)} pi(floor(10^n/k)) - floor(sqrt(10^n))*pi(floor(sqrt(10^n))).

a(n) = A241419(10^n).

a(n) = A064182(n) - Sum_{prime p <= sqrt(10^n)} floor(10^n/p).

Example

a(1) = 3, because there are three values of m = {5, 7, 10} that have prime divisors that exceed sqrt(10^1)=3.162... These prime divisors are {5, 7, 5} respectively.

Mathematica

Table[Sum[PrimePi[Quotient[10^n, k]], {k, 1, 10^(n/2)}], {n, 0, 8}] - Table[Floor[10^(n/2)]*PrimePi[Floor[10^(n/2)]], {n, 0, 8}]

Crossrefs

Cf. A006530, A241419, A064182.

Sequence in context: A068380 A174782 A345074 * A119294 A157541 A374522

Adjacent sequences: A390599 A390600 A390601 * A390603 A390604 A390605

Keyword

nonn

Author

Henri Lifchitz, Nov 12 2025

Status

approved