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A292376
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a(1) = 0, a(2n) = 0, and for odd numbers n > 1, a(n) = a(A064989(n)) + [n == 3 (mod 4)].
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3
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0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 4, 0, 0, 0, 5, 0, 0, 0, 1, 0, 5, 0, 6, 0, 0, 0, 2, 0, 6, 0, 1, 0, 6, 0, 7, 0, 0, 0, 8, 0, 0, 0, 1, 0, 8, 0, 1, 0, 0, 0, 9, 0, 9, 0, 1, 0, 0, 0, 10, 0, 0, 0, 11, 0, 11, 0, 1, 0, 2, 0, 12, 0, 0, 0, 13, 0, 1, 0, 1, 0, 13, 0, 2, 0, 0, 0, 2, 0, 13, 0, 1, 0, 13, 0, 14, 0, 0
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OFFSET
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1,7
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COMMENTS
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For odd numbers > 1, iterate the map x -> A064989(x), which shifts every prime in the prime factorization of n one index step towards smaller primes. a(n) counts the numbers of the form 4k+3 encountered until the first number which is even has been reached. This count includes also n itself if it is of the form 4k+3 (A004767).
In other words, locate the position where n is in square array A246278 and moving up by that column, count all numbers of the form 4k+3 before an even number at the top of the column is reached.
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LINKS
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FORMULA
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a(1) = 0, a(2n) = 0, and for odd numbers n > 1, a(n) = a(A064989(n)) + floor((n mod 4)/3).
Other identities and observations. For n >= 1.
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MATHEMATICA
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a[1] = 0; a[n_] := a[n] = If[EvenQ@ n, 0, a[Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n] + Boole[Mod[n, 4] == 3]]; Array[a, 105] (* Michael De Vlieger, Sep 17 2017 *)
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PROG
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(Scheme, with memoization-macro definec)
(definec (A292376 n) (if (or (even? n) (= 1 n)) 0 (+ (floor->exact (/ (modulo n 4) 3)) (A292376 (A064989 n)))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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