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A106315 Harmonic residue of n. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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.
LINKS
FORMULA
a(n) = A038040(n) - A000203(n) * A240471(n) . - Reinhard Zumkeller, Apr 06 2014
MAPLE
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
MATHEMATICA
HarmonicResidue[n_]=Mod[n*DivisorSigma[0, n], DivisorSigma[1, n]]; HarmonicResidue[ Range[ 80]]
PROG
(Haskell)
a106315 n = n * a000005 n `mod` a000203 n -- Reinhard Zumkeller, Apr 06 2014
CROSSREFS
Cf. A106316, A106317, A001599 (positions of zeros).
Sequence in context: A191474 A199602 A324057 * A285295 A217563 A254881
KEYWORD
nonn
AUTHOR
George J. Schaeffer (gschaeff(AT)andrew.cmu.edu), Apr 29 2005
EXTENSIONS
Mathematica program completed by Harvey P. Dale, Feb 29 2024
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)