

A071825


(Number of x with largest prime factor of the form 4k+3 less than or equal to n) minus (Number of x with largest prime factor of the form 4k+1 less than or equal to n).


0



0, 1, 1, 0, 1, 2, 2, 3, 2, 3, 4, 3, 4, 3, 3, 2, 3, 4, 3, 4, 5, 6, 7, 6, 5, 6, 7, 6, 5, 6, 6, 7, 6, 7, 8, 7, 8, 7, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 10, 11, 10, 9, 10, 11, 11, 10, 11, 12, 11, 12, 13, 14, 15, 14, 13, 12, 13, 14, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15
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OFFSET

1,6


COMMENTS

Weak conjecture: sequence gives positive values only; strong conjecture: for n large enough a(n) > 2*sqrt(n).


LINKS

Table of n, a(n) for n=1..87.


FORMULA

a(n) = Card( x<=n : A006530(x) == 3 mod 4)  Card( x<=n : A006530(x) == 1 mod 4)


PROG

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


CROSSREFS

Sequence in context: A147952 A091316 A321862 * A115727 A115726 A086413
Adjacent sequences: A071822 A071823 A071824 * A071826 A071827 A071828


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Jun 07 2002


STATUS

approved



