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A063441
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Sum_{d|n} d *mu(n), sigma(n) * mu(n).
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7
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1, -3, -4, 0, -6, 12, -8, 0, 0, 18, -12, 0, -14, 24, 24, 0, -18, 0, -20, 0, 32, 36, -24, 0, 0, 42, 0, 0, -30, -72, -32, 0, 48, 54, 48, 0, -38, 60, 56, 0, -42, -96, -44, 0, 0, 72, -48, 0, 0, 0, 72, 0, -54, 0, 72, 0, 80, 90, -60, 0, -62, 96, 0, 0, 84, -144, -68, 0, 96, -144, -72, 0, -74, 114, 0, 0, 96, -168, -80, 0, 0, 126, -84, 0, 108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,2000
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FORMULA
| a(n) = A003959(n)*A008683(n) if n squarefree, 0 else. - R. Stephan, Mar 26 2004
a(n) = A000203(n)*A008683(n).
Multiplicative with a(p^e) = -p-1, if e = 1, 0 otherwise. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 27, 2005, sign flipped by R. J. Mathar, May 29 2011
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EXAMPLE
| n=6: divisors of 6 are = [1, 2, 3, 6] and 1 * mu(6) + 2 * mu(6) + 3 * mu(6) + 6 * mu(6) = 12.
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PROG
| (PARI) j=[]; for(n=1, 200, j=concat(j, sumdiv(n, d, d*moebius(n)))); j
(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1-X-p*X)[n]) (from R. Stephan)
(PARI) { for (n=1, 2000, write("b063441.txt", n, " ", direuler(p=2, n, 1-X-p*X)[n]) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 21 2009]
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CROSSREFS
| Sequence in context: A105576 A105826 A110665 * A092894 A011338 A049251
Adjacent sequences: A063438 A063439 A063440 * A063442 A063443 A063444
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KEYWORD
| easy,sign,mult
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jul 23 2001
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