A267113 Bitwise-OR of the exponents of all 4k+1 primes in the prime factorization of n.

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

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