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A277328 Number of primes (counted with multiplicity) dividing gcd(A260443(n), A260443(n+1)): a(n) = A001222(A277198(n)). 7

%I

%S 0,0,1,0,0,1,2,0,0,2,2,1,1,2,3,0,0,3,3,1,1,4,4,1,1,4,4,2,2,3,4,0,0,4,

%T 4,3,2,5,6,1,1,7,6,2,3,6,6,1,1,6,6,3,3,7,7,2,2,6,6,3,3,4,5,0,0,5,5,4,

%U 4,8,8,2,2,9,9,4,4,8,9,1,1,10,9,5,5,10,11,2,2,11,10,5,6,8,8,1,1,8,8,5,4,10,11,3,3,12

%N Number of primes (counted with multiplicity) dividing gcd(A260443(n), A260443(n+1)): a(n) = A001222(A277198(n)).

%H Antti Karttunen, <a href="/A277328/b277328.txt">Table of n, a(n) for n = 0..8192</a>

%F a(n) = A001222(A277198(n)).

%F a(n) >= A277327(n).

%o (Scheme)

%o (define (A277328 n) (A001222 (A277198 n)))

%o ;; A standalone implementation:

%o (define (A277328 n) (reduce + 0 (gcd_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n)))))

%o (definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))

%o (define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

%o (define (gcd_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (gcd_of_exp_lists nums2 nums1)) (else (map min nums1 (append nums2 (make-list (- len1 len2) 0)))))))

%Y Cf. A001222, A125184, A260443, A277198, A277327.

%K nonn,look

%O 0,7

%A _Antti Karttunen_, Oct 13 2016

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Last modified December 12 17:50 EST 2019. Contains 329960 sequences. (Running on oeis4.)