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A107759
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a(n) = (+2)UnitarySigma(n): if n = Product p_i^r_i then a(n) = Product (2 + p_i^r_i).
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9
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1, 4, 5, 6, 7, 20, 9, 10, 11, 28, 13, 30, 15, 36, 35, 18, 19, 44, 21, 42, 45, 52, 25, 50, 27, 60, 29, 54, 31, 140, 33, 34, 65, 76, 63, 66, 39, 84, 75, 70, 43, 180, 45, 78, 77, 100, 49, 90, 51, 108, 95, 90, 55, 116, 91
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OFFSET
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1,2
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/12) * Product_{p prime} (1 + 1/p^2 - 2/p^3) = A072691 * A330594 = 0.910438... . - Amiram Eldar, Nov 01 2022
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EXAMPLE
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a(12) = (2+3)*(2+4) = 30.
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MAPLE
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A107759 := proc(n) local pf, p ; if n = 1 then 1; else pf := ifactors(n)[2] ; mul( 2+op(1, p)^op(2, p), p=pf) ; end if; end proc:
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MATHEMATICA
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a[1] = 1; a[n_] := Times @@ (2 + Power @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 20 2020 *)
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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