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A193529
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Sum of odd divisors of sopf(n).
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1
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0, 1, 4, 1, 6, 6, 8, 1, 4, 8, 12, 6, 14, 13, 1, 1, 18, 6, 20, 8, 6, 14, 24, 6, 6, 24, 4, 13, 30, 6, 32, 1, 8, 20, 4, 6, 38, 32, 1, 8, 42, 4, 44, 14, 1, 31, 48, 6, 8, 8, 6, 24, 54, 6, 1, 13, 12, 32, 60, 6, 62, 48, 6, 1, 13, 1, 68, 20, 14, 8, 72, 6, 74, 56, 1
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 6 because sopf(5) = 5, and the sum of the 2 odd divisors of 5, {1, 5}, is 6.
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MATHEMATICA
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Table[Total[Select[Divisors[Plus@@First[Transpose[FactorInteger[n]]]], OddQ[#]&]], {n, 100}]
sopf[n_] := Total[FactorInteger[n][[;; , 1]]]; oddsigma[n_] := DivisorSigma[1, n/2^IntegerExponent[n, 2]]; a[1] = 0; a[n_] := oddsigma[sopf[n]]; Array[a, 100] (* Amiram Eldar, May 18 2023 *)
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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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