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0, 1, 0, 2, 0, 1, 1, 3, -3, 1, 1, 2, 1, 2, -1, 4, 3, -2, 3, 2, 0, 2, 4, 3, -7, 2, -2, 3, 5, 0, 6, 5, 0, 4, -1, -1, 3, 4, 0, 3, 7, 1, 7, 3, -3, 5, 9, 4, -4, -6, 2, 3, 11, -1, 0, 4, 2, 6, 11, 1, 6, 7, -3, 6, 0, 1, 10, 5, 3, 0, 14, 0, 8, 4, -8, 5, -1, 1, 15, 4, -1, 8, 16, 2, 2, 8, 4, 4, 18, -2, -1, 6, 5, 10, 2, 5, 19
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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LINKS
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FORMULA
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For all n >= 0, a(2^n) = n.
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MATHEMATICA
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f[p_, e_] := If[p == 2, 1, NextPrime[p, -1]^e]; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; h[1] = 0; h[n_] := h[n] = If[EvenQ[n], h[n/2] + 1, h[g[n]] + 1]; a[n_] := h[n] - h[DivisorSigma[1, n/2^IntegerExponent[n, 2]]]; Array[a, 100] (* Amiram Eldar, Sep 19 2021 *)
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PROG
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(PARI)
A000593(n) = sigma(n>>valuation(n, 2));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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