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A033634
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OddPowerSigma(n) = sum of odd power divisors of n
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2
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1, 3, 4, 3, 6, 12, 8, 11, 4, 18, 12, 12, 14, 24, 24, 11, 18, 12, 20, 18, 32, 36, 24, 44, 6, 42, 31, 24, 30, 72, 32, 43, 48, 54, 48, 12, 38, 60, 56, 66, 42, 96, 44, 36, 24, 72, 48, 44, 8, 18, 72, 42, 54, 93, 72, 88, 80, 90, 60, 72, 62, 96, 32, 43, 84, 144, 68, 54, 96, 144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| If n = Product p(i)^r(i) then opsigma(n) = Product (1+(p(i)^(s(i)+2)-p(i))/(p(i)^2-1)), where si=ri when ri is odd, si=ri-1 when ri is even.
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MAPLE
| A033634 := proc(n) a := 1 ; for d in ifactors(n)[2] do if type(op(2, d), 'odd') then s := op(2, d) ; else s := op(2, d)-1 ; end if; p := op(1, d) ; a := a*(1+(p^(s+2)-p)/(p^2-1)) ; end do: a; end proc:
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CROSSREFS
| Sequence in context: A109506 A000113 A069915 * A111970 A141730 A127737
Adjacent sequences: A033631 A033632 A033633 * A033635 A033636 A033637
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KEYWORD
| nonn,mult
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AUTHOR
| Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
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