A091372 Number of numbers <= n having more prime factors than the value of their smallest prime factor.

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 27

Offset

1,12

Comments

a(n) = #{m: A001222(m)>A020639(m), m<=n};

a(n) + A091373(n) + A091374(n) = n.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

For any k < 1, a(n) > kn for large enough k. For example, a(n) > n/2 for n > 26474. - Charles R Greathouse IV, Jul 06 2016

Mathematica

Accumulate@ Boole@ Map[Length@ Flatten[Table[#1, {#2}] & @@@ #] > #[[1, 1]] &@ FactorInteger@ # &, Range@ 80] (* Michael De Vlieger, Jul 06 2016 *)

Prog

(PARI) a(n)=sum(k=8, n, bigomega(k) > factor(k)[1, 1]) \\ Charles R Greathouse IV, Jul 06 2016
(PARI) first(n)=my(v=vector(n), s); for(k=8, n, v[k] = s += bigomega(k) > factor(k)[1, 1]); v \\ Charles R Greathouse IV, Jul 06 2016

Crossrefs

Cf. A091375, A091371.

Sequence in context: A116563 A076695 A071903 * A185322 A324918 A068980

Adjacent sequences: A091369 A091370 A091371 * A091373 A091374 A091375

Keyword

nonn

Author

Reinhard Zumkeller, Jan 04 2004

Status

approved