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A136025
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Sum of distinct proper prime divisors of odd integers below 10^n.
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2
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3, 373, 24307, 1691682, 127867801, 10233538789, 850896280551, 72812857079241, 6363727756215813, 565232434009370012, 50843507342073211151
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Through 10^5 about 37.5 percent of total sums for all integers N comprise sums of odd N and the remaining 62.5 percent to even N.
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FORMULA
| a(n) = sum_{k=1,2,...,A093143(n)} A105221(2k-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 29 2008
a(n) = sum_{prime p, 3<=p<10^n} p*floor((10^n-p)/(2p)). [From Max Alekseyev]
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EXAMPLE
| a(0)=3 because the only odd N <=10^1-1 having a prime factor is 9 and its factor is 3 and sum is 3.
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MAPLE
| A105221 := proc(n) local a, ifs, p; ifs := ifactors(n)[2] ; a := 0 ; for p in ifs do if op(1, p) <> 1 and op(1, p) <> n then a := a+op(1, p) ; fi ; od: RETURN(a) ; end: A136025 := proc(n) local a, k ; a := 0 ; for k from 5 to 10^n-1 by 2 do a := a+A105221(k) ; od: RETURN(a) ; end: for n from 1 do print(A136025(n)); od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 29 2008
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CROSSREFS
| Cf. A136021, A136024, A143851
Sequence in context: A173648 A110717 A068988 * A157577 A062604 A160192
Adjacent sequences: A136022 A136023 A136024 * A136026 A136027 A136028
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KEYWORD
| more,nonn
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AUTHOR
| Enoch Haga (Enokh(AT)comcast.net), Dec 12 2007
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EXTENSIONS
| a(6) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 29 2008
a(7)-a(11) from Max Alekseyev (maxale(AT)gmail.com), Jan 30 2012
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