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A069290
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Sum of square roots of square divisors of n.
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4
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1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 7, 1, 4, 1, 3, 1, 1, 1, 3, 6, 1, 4, 3, 1, 1, 1, 7, 1, 1, 1, 12, 1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 7, 8, 6, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 4, 15, 1, 1, 1, 3, 1, 1, 1, 12, 1, 1, 6, 3, 1, 1, 1, 7, 13, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 7, 1, 8, 4, 18, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(m)=1 iff m is squarefree (A005117).
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LINKS
| Nick Hobson, Table of n, a(n) for n = 1..1000
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FORMULA
| Multiplicative with a(p^e) = (p^(floor(e/2)+1)-1)/(p-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 23 2002
G.f.: Sum( k>=0, k*x^k^2/(1-x^k^2) ). - Ralf Stephan, Apr 21 2003
Dirichlet g.f. zeta(2s-1)*zeta(s). Inverse Mobius transform of A037213. - R. J. Mathar, Oct 31 2011
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EXAMPLE
| Square divisors for n=48: {1, 2^2, 4^2}, so a(48)=1+2+4=7.
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PROG
| (PARI) vector(102, n, sumdiv(n, d, issquare(d)*sqrtint(d)))
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CROSSREFS
| Cf. A035316, A000188, A046951.
Sequence in context: A166030 A191523 A132890 * A076476 A016733 A060234
Adjacent sequences: A069287 A069288 A069289 * A069291 A069292 A069293
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KEYWORD
| nonn,easy,mult
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 14 2002
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Jul 01 2002
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