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Search: id:A069184
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| A069184 |
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Sum of divisors d of n such that d or n/d is odd. |
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+0
4
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| 1, 3, 4, 5, 6, 12, 8, 9, 13, 18, 12, 20, 14, 24, 24, 17, 18, 39, 20, 30, 32, 36, 24, 36, 31, 42, 40, 40, 30, 72, 32, 33, 48, 54, 48, 65, 38, 60, 56, 54, 42, 96, 44, 60, 78, 72, 48, 68, 57, 93, 72, 70, 54, 120, 72, 72, 80, 90, 60, 120, 62, 96, 104, 65, 84, 144, 68, 90, 96
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Might be called UnitaryOrdinarySigma(n): If n=Product p_i^r_i then UOSigma(n)=UnitarySigma(2^r_1)*Sigma(n/2^r_1)=(2^r_1+1)*Product (p_i^(r_i+1)-1)/(p_i-1), p_i is not 2. - Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Jun 11 2005
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FORMULA
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Multiplicative with a(2^e) = 2^e+1 and a(p^e) = (p^(e+1)-1)/(p-1) for an odd prime p.
G.f.: Sum_{m>0} m*x^m*(1+x^m+x^(2*m)-x^(3*m))/(1-x^(4*m)).
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EXAMPLE
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UOSigma(2^4*7^2)=UnitarySigma(2^4)*sigma(7^2)=17*57=969
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CROSSREFS
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Cf. A069733, A107749, A092356.
Sequence in context: A103402 A154664 A034448 this_sequence A049417 A125139 A107224
Adjacent sequences: A069181 A069182 A069183 this_sequence A069185 A069186 A069187
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KEYWORD
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mult,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2002
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar
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