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A336361
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Number of iterations of A000593 (sum of divisors of odd part of n) needed to reach a power of 2, or -1 if never reached.
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13
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0, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 2, 0, 4, 3, 3, 2, 1, 2, 2, 1, 2, 2, 3, 1, 3, 2, 1, 0, 2, 4, 2, 3, 4, 3, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 4, 2, 4, 2, 4, 3, 4, 1, 3, 3, 3, 2, 2, 1, 3, 0, 2, 2, 5, 4, 2, 2, 4, 3, 5, 4, 2, 3, 2, 2, 3, 2, 5, 2, 2, 1, 4, 3, 3, 2, 4, 3, 2, 2, 1, 2, 3, 1, 5, 4, 3, 2, 5, 4, 3, 2, 2
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OFFSET
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1,5
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COMMENTS
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Also, for n > 1, one less than the number of iterations of A000593 to reach 1.
If there exists any hypothetical odd perfect numbers w, then the iteration will get stuck into a fixed point after encountering them, and we will have a(w) = a(2^k * w) = -1 by the escape clause.
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LINKS
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FORMULA
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If A209229(n) = 1 [when n is a power of 2], a(n) = 0, otherwise a(n) = 1+a(A000593(n)).
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PROG
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(PARI) A336361(n) = if(!bitand(n, n-1), 0, 1+A336361(sigma(n>>valuation(n, 2))));
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CROSSREFS
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Cf. A054784 (positions of 0's and 1's in this sequence).
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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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