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A365337
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The sum of divisors of the largest exponentially odd number dividing n.
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1
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1, 3, 4, 3, 6, 12, 8, 15, 4, 18, 12, 12, 14, 24, 24, 15, 18, 12, 20, 18, 32, 36, 24, 60, 6, 42, 40, 24, 30, 72, 32, 63, 48, 54, 48, 12, 38, 60, 56, 90, 42, 96, 44, 36, 24, 72, 48, 60, 8, 18, 72, 42, 54, 120, 72, 120, 80, 90, 60, 72, 62, 96, 32, 63, 84, 144, 68
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OFFSET
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1,2
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COMMENTS
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The number of divisors of the largest exponentially odd number dividing n is A286324(n).
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p^(e+1)-1)/(p-1) if e is odd and (p^e-1)/(p-1) if e is even.
Dirichlet g.f.: zeta(s) * zeta(2*s-2) * Product_{p prime} (1 + 1/p^(s-1) - 1/p^(2*s-2) + 1/p^(3*s-2)).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 + 1/(p*(p^2-1))) = 1.2312911488886... (A065487). - Amiram Eldar, Sep 01 2023
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MATHEMATICA
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f[p_, e_] := (p^(e + Mod[e, 2]) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + f[i, 2]%2) - 1)/(f[i, 1] - 1)); }
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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