A071825 a(n) = (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

Offset

1,7

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..88.

Formula

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

a(n) = A071823(n) - A071824(n). - Sean A. Irvine, Aug 16 2024

Prog

(PARI) for(n=1, 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

Cf. A071823, A071824.

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

Extensions

Missing a(1)=0 inserted by Sean A. Irvine, Aug 16 2024

Status

approved