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A267113 Bitwise-OR of the exponents of all 4k+1 primes in the prime factorization of n. 6
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,25

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A267116(A170818(n)).

Other identities. For all n >= 0:

a(n) = a(A170818(n)). [The result depends only on the prime factors of the form 4k+1.]

a(n) <= A083025(n).

EXAMPLE

For n = 65 = 5 * 13 = (4+1)^1 * ((3*4)+1)^1, bitwise-or of 1 and 1 is 1, thus a(65) = 1.

PROG

(Scheme, with memoization-macro definec)

(definec (A267113 n) (cond ((< n 5) 0) ((even? n) (A267113 (/ n 2))) ((= 3 (modulo (A020639 n) 4)) (A267113 (A032742 n))) (else (A003986bi (A067029 n) (A267113 (A028234 n)))))) ;;  A003986bi implements bitwise-or (see A003986).

CROSSREFS

Cf. A170818, A267116, A260728.

Cf. A004144 (indices of zeros), A009003 (of nonzeros).

Differs from both A046080 and A083025 for the first time at n=65, which here a(65) = 1.

Sequence in context: A279278 A015964 A088950 * A083025 A046080 A170967

Adjacent sequences:  A267110 A267111 A267112 * A267114 A267115 A267116

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 03 2016

STATUS

approved

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Last modified October 14 16:29 EDT 2019. Contains 328022 sequences. (Running on oeis4.)