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A107749
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OrdinaryUnitarySigma(n): If n = Product p_i^r_i then OUSigma(n) = Sigma(2^r_1)*UnitarySigma(n/2^r_1).
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5
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1, 3, 4, 7, 6, 12, 8, 15, 10, 18, 12, 28, 14, 24, 24, 31, 18, 30, 20, 42, 32, 36, 24, 60, 26, 42, 28, 56, 30, 72, 32, 63, 48, 54, 48, 70, 38, 60, 56, 90, 42, 96, 44, 84, 60, 72, 48, 124, 50, 78, 72, 98, 54, 84, 72, 120, 80, 90, 60, 168, 62, 96, 80, 127, 84, 144, 68, 126, 96
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OFFSET
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1,2
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A000203(p2) * A034448(n/p2), where p2 = A006519(n). - R. J. Mathar, Jun 15 2008
Multiplicative with a(2^e) = 2^(e+1)-1, a(p^e) = p^e+1 for p>2, e>0.
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EXAMPLE
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OUSigma(2^4*7^2) = Sigma(2^4)*UnitarySigma(7^2) = 31*50 = 1550.
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MAPLE
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A107749 := proc(n) local a, f, p, e; a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; if p = 2 then a := a*(2^(e+1)-1) ; else a := a*(p^e+1) ; end if; end do; a ; end proc: # R. J. Mathar, Jun 02 2011
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MATHEMATICA
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f[2, e_] := 2^(e+1)-1; f[p_, e_] := p^e+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 15 2020 *)
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PROG
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(PARI) a(n)=local(fm); fm=factor(n); prod(k=1, matsize(fm)[1], if(fm[k, 1]==2, 2^(fm[k, 2]+1)-1, fm[k, 1]^fm[k, 2]+1))
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CROSSREFS
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Cf. A069184, A091321, A000203, A034448, A006519.
Sequence in context: A051378 A254981 A116607 * A093811 A088000 A284344
Adjacent sequences: A107746 A107747 A107748 * A107750 A107751 A107752
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KEYWORD
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nonn,mult
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AUTHOR
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Yasutoshi Kohmoto, Jun 11 2005, Feb 24 2007
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EXTENSIONS
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Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007
More terms from R. J. Mathar, Jun 15 2008
Name corrected by Franklin T. Adams-Watters, Aug 24 2013
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STATUS
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approved
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