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A091570
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Sum of odd proper divisors of n. Sum of the odd divisors of n that are less than n.
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14
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0, 1, 1, 1, 1, 4, 1, 1, 4, 6, 1, 4, 1, 8, 9, 1, 1, 13, 1, 6, 11, 12, 1, 4, 6, 14, 13, 8, 1, 24, 1, 1, 15, 18, 13, 13, 1, 20, 17, 6, 1, 32, 1, 12, 33, 24, 1, 4, 8, 31, 21, 14, 1, 40, 17, 8, 23, 30, 1, 24, 1, 32, 41, 1, 19, 48, 1, 18, 27, 48, 1, 13, 1, 38, 49
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OFFSET
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1,6
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} (2*k-1) * x^(4*k-2) / (1 - x^(2*k-1)). - Ilya Gutkovskiy, Apr 13 2021
Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(2)-1)/4 = 0.1612335167... . - Amiram Eldar, Oct 11 2023
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EXAMPLE
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The sum of odd divisors of 9 that are less than 9 is 1 + 3 = 4.
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MATHEMATICA
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f[2, e_] := 1; f[p_, e_] := (p^(e+1)-1)/(p-1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n, 0]; Array[a, 75] (* Amiram Eldar, Oct 11 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n , d, (d%2) * (d<n) * d); \\ Michel Marcus, Jan 14 2014
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CROSSREFS
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Sum of the k-th powers of the odd proper divisors of n for k=0..10: A091954 (k=0), this sequence (k=1), A351647 (k=2), A352031 (k=3), A352032 (k=4), A352033 (k=5), A352034 (k=6), A352035 (k=7), A352036 (k=8), A352037 (k=9), A352038 (k=10).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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