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A069733
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Number of divisors m of n such that m or n/m is odd. Number of non-orientable coverings of the Klein bottle with n lists.
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4
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1, 2, 2, 2, 2, 4, 2, 2, 3, 4, 2, 4, 2, 4, 4, 2, 2, 6, 2, 4, 4, 4, 2, 4, 3, 4, 4, 4, 2, 8, 2, 2, 4, 4, 4, 6, 2, 4, 4, 4, 2, 8, 2, 4, 6, 4, 2, 4, 3, 6, 4, 4, 2, 8, 4, 4, 4, 4, 2, 8, 2, 4, 6, 2, 4, 8, 2, 4, 4, 8, 2, 6, 2, 4, 6, 4, 4, 8, 2, 4, 5, 4, 2, 8, 4, 4, 4, 4, 2, 12, 4, 4, 4, 4, 4, 4, 2, 6, 6, 6, 2, 8, 2, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Multiplicative defined by f(2^k)=2 and f(p^k)=k+1 for k>0 and an odd prime p.
Also number of divisors of n that are not divisible by 4. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 16 2002
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LINKS
| V. A. Liskovets and A. Mednykh, Number of non-orientable coverings of the Klein bottle
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FORMULA
| a(n) == d(n)-d(n/4) for 4|n and =d(n) otherwise where d(n) is the number of divisors of n (A000005).
G.f.: Sum_{m>0} x^m*(1+x^m+x^(2*m))/(1-x^(4*m)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 21 2002
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PROG
| (PARI) a(n)=if(n<1, 0, sumdiv(n, d, sign(d%4)))
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CROSSREFS
| Cf. A069184.
Cf. A046897.
Sequence in context: A183095 A127973 A023157 * A187467 A081755 A097859
Adjacent sequences: A069730 A069731 A069732 * A069734 A069735 A069736
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KEYWORD
| mult,easy,nonn
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AUTHOR
| Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002
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