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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.)