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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)=(2^(r_1+1)-1)*Product(p_i^r_i+1), p_i is not 2.
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)= A000203(p2)*A034448(n/p2) where p2=A006519(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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
| OUSigma(2^4*7^2)=Sigma(2^4)*UnitarySigma(7^2)=31*50=1550.
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MAPLE
| 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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PROG
| (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
| Cf. A069184, A091321, A000203, A034448, A006519.
Sequence in context: A049418 A051378 A116607 * A093811 A088000 A168338
Adjacent sequences: A107746 A107747 A107748 * A107750 A107751 A107752
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KEYWORD
| nonn,mult
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AUTHOR
| Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Jun 11 2005, Feb 24 2007
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 08 2007
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2008
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