A071823 - OEIS

A071823

Number of numbers x <= n with largest prime factor of the form 4k+3.

0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 12, 13, 13, 13, 14, 15, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 20, 20, 21, 22, 23, 23, 24, 25, 26, 27, 27, 27, 27, 27, 28, 29, 30, 31, 31, 32, 32, 32, 33, 34, 34, 34, 35, 36, 36, 37, 38, 39, 40, 40, 40, 40, 41

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

Conjecture : for n > 1000, a(n) - n/2 > sqrt(n).

LINKS

Table of n, a(n) for n=1..76.

MATHEMATICA

Accumulate[Table[If[Mod[FactorInteger[n][[-1, 1]], 4]==3, 1, 0], {n, 80}]] (* Harvey P. Dale, Jun 29 2017 *)

PROG

(PARI) for(n=2, 200, print1(sum(i=2, n, if((component(component(factor(i), 1), omega(i))-3)%4, 0, 1)), ", "))

CROSSREFS