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A341621
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a(n) is the exponent of the least power of 2 that when multiplied by n makes the product abundant, or -1 if n itself is a power of 2.
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2
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-1, -1, 2, -1, 2, 1, 3, -1, 1, 1, 3, 0, 3, 2, 1, -1, 4, 0, 4, 0, 1, 2, 4, 0, 2, 2, 1, 1, 4, 0, 5, -1, 1, 3, 1, 0, 5, 3, 1, 0, 5, 0, 5, 1, 1, 3, 5, 0, 2, 1, 1, 1, 5, 0, 2, 0, 1, 3, 5, 0, 5, 4, 1, -1, 2, 0, 6, 2, 1, 0, 6, 0, 6, 4, 1, 2, 2, 0, 6, 0, 1, 4, 6, 0, 2, 4, 1, 0, 6, 0, 2, 2, 1, 4, 2, 0, 6, 1, 1, 0, 6, 0, 6, 0, 1
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OFFSET
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1,3
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COMMENTS
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Number of iterations of x -> 2x needed before the result is abundant (sigma(x) > 2x), when starting from x=n, or -1 if an abundant number would never be reached (when n is a power of 2).
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LINKS
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MATHEMATICA
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a[n_] := Module[{e = IntegerExponent[n, 2], s}, If[n == 2^e, -1, s = DivisorSigma[-1, n/2^e]; Max[Floor[Log2[s/(s - 1)]] - e, 0]]]; Array[a, 100] (* Amiram Eldar, Apr 01 2024 *)
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PROG
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(PARI) A341621(n) = if(!bitand(n, n-1), -1, for(i=0, oo, my(n2 = n+n); if(sigma(n) > n2, return(i)); n = n2));
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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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