

A091372


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


5



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
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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 A068980 A053266
Adjacent sequences: A091369 A091370 A091371 * A091373 A091374 A091375


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jan 04 2004


STATUS

approved



