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Search: id:A107749
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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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+0
3
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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; listen)
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OFFSET
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1,2
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FORMULA
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a(n)= A000203(p2)*A034448(n/p2) where p2=A006519(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2008
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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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A034448 := proc(n) local ifs, d ; if n = 1 then 1; else ifs := ifactors(n)[2] ; mul(1+ op(1, op(d, ifs))^op(2, op(d, ifs)), d=1..nops(ifs)) ; fi ; end: A006519 := proc(n) local i ; for i in ifactors(n)[2] do if op(1, i) = 2 then RETURN( op(1, i)^op(2, i) ) ; fi ; od: RETURN(1) ; end: A107749 := proc(n) local p2 ; p2 := A006519(n) ; numtheory[sigma](p2)*A034448(n/p2) ; end: seq(A107749(n), n=1..100) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2008
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CROSSREFS
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Cf. A069184, A091321.
Sequence in context: A049418 A051378 A116607 this_sequence A093811 A088000 A034690
Adjacent sequences: A107746 A107747 A107748 this_sequence 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 (zbi74583(AT)boat.zero.ad.jp), Jun 11 2005, Feb 24 2007
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EXTENSIONS
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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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