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A106315
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Harmonic residue of n.
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15
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0, 1, 2, 5, 4, 0, 6, 2, 1, 4, 10, 16, 12, 8, 12, 18, 16, 30, 18, 36, 20, 16, 22, 12, 13, 20, 28, 0, 28, 24, 30, 3, 36, 28, 44, 51, 36, 32, 44, 50, 40, 48, 42, 12, 36, 40, 46, 108, 33, 21, 60, 18, 52, 72, 4, 88, 68, 52, 58, 48, 60, 56, 66, 67, 8, 96, 66, 30, 84, 128, 70, 84, 72, 68, 78
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OFFSET
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1,3
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COMMENTS
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The harmonic residue is the remainder when n*d(n) is divided by sigma(n), where d(n) is the number of divisors of n and sigma(n) is the sum of the divisors of n. If n is perfect, the harmonic residue of n is 0.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A038040(n) - A000203(n) * A240471(n) . - Reinhard Zumkeller, Apr 06 2014
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MAPLE
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A106315 := proc(n)
modp(n*numtheory[tau](n), numtheory[sigma](n)) ;
end proc:
seq(A106315(n), n=1..100) ; # R. J. Mathar, Jan 25 2017
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MATHEMATICA
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HarmonicResidue[n_]=Mod[n*DivisorSigma[0, n], DivisorSigma[1, n]]
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PROG
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(Haskell)
a106315 n = n * a000005 n `mod` a000203 n -- Reinhard Zumkeller, Apr 06 2014
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CROSSREFS
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Cf. A106316, A106317, A001599 (positions of zeros).
Cf. A000005, A000203.
Sequence in context: A191474 A199602 A324057 * A285295 A217563 A254881
Adjacent sequences: A106312 A106313 A106314 * A106316 A106317 A106318
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KEYWORD
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nonn
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AUTHOR
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George J. Schaeffer (gschaeff(AT)andrew.cmu.edu), Apr 29 2005
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STATUS
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approved
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