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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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5
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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)).
Dirichlet g.f. zeta(s) *zeta(s-1) *(2^(2-3s)-2^(1-2s)-2^(1-s)+1) / (1-2^(1-s)). - R. J. Mathar, Jun 02 2011
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EXAMPLE
| UOSigma(2^4*7^2)=UnitarySigma(2^4)*sigma(7^2)=17*57=969
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MAPLE
| A069184 := 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) ; else a := a*(p^(e+1)-1)/(p-1) ; end if; end do; a ; end proc: # R. J. Mathar, Jun 02 2011
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CROSSREFS
| Cf. A069733, A107749, A092356.
Sequence in context: A154664 A191750 A034448 * A181549 A049417 A188999
Adjacent sequences: A069181 A069182 A069183 * A069185 A069186 A069187
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KEYWORD
| mult,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2002
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EXTENSIONS
| 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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