login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260728 Bitwise-OR of the exponents of all 4k+3 primes in the prime factorization of n. 8
0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 3, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 0, 0, 3, 1, 1, 1, 0, 1, 1, 0, 1, 3, 0, 0, 1, 1, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 4, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 2, 3, 0, 0, 1, 1, 0, 1, 0, 1, 3, 0, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

A001481 (numbers that are the sum of 2 squares) gives the positions of even terms in this sequence, while its complement A022544 (numbers that are not the sum of 2 squares) gives the positions of odd terms.

If instead of bitwise-oring (A003986) we added in ordinary way the exponents of 4k+3 primes together, we would get the sequence A065339. For the positions where these two sequences differ see A260730.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

FORMULA

If n < 3, a(n) = 0; thereafter, for any even n: a(n) = a(n/2), for any n with its smallest prime factor (A020639) of the form 4k+1: a(n) = a(A032742(n)), otherwise [when A020639(n) is of the form 4k+3] a(n) = A003986(A067029(n),a(A028234(n))).

Other identities. For all n >= 0:

A229062(n) = 1 - A000035(a(n)). [Reduced modulo 2 and complemented, the sequence gives the characteristic function of A001481.]

a(n) = a(A097706(n)). [The result depends only on the prime factors of the form 4k+3.]

a(n) = A267116(A097706(n)).

a(n) = A267113(A267099(n)).

EXAMPLE

For n = 21 = 3^1 * 7^1 we compute A003986(1,1) = 1, thus a(21) = 1.

For n = 63 = 3^2 * 7^1 we compute A003986(2,1) = A003986(1,2) = 3, thus a(63) = 3.

MATHEMATICA

Table[BitOr @@ (Map[Last, FactorInteger@ n /. {p_, _} /; MemberQ[{0, 1, 2}, Mod[p, 4]] -> Nothing]), {n, 0, 120}] (* Michael De Vlieger, Feb 07 2016 *)

PROG

(Scheme) (define (A260728 n) (cond ((< n 3) 0) ((even? n) (A260728 (/ n 2))) ((= 1 (modulo (A020639 n) 4)) (A260728 (A032742 n))) (else (A003986bi (A067029 n) (A260728 (A028234 n)))))) ;; A003986bi implements bitwise-or (see A003986).

CROSSREFS

Cf. A000035, A001481, A022544, A003986, A020639, A028234, A032742, A067029, A097706, A229062, A260730.

Cf. also A267113, A267116, A267099.

Differs from A065339 for the first time at n=21, where a(21) = 1, while A065339(21)=2.

Sequence in context: A116377 A131964 A091430 * A065339 A122434 A141571

Adjacent sequences:  A260725 A260726 A260727 * A260729 A260730 A260731

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 12 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 18:44 EDT 2019. Contains 327180 sequences. (Running on oeis4.)