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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 Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 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]] PROG (Haskell) a106315 n = n * a000005 n `mod` a000203 n -- Reinhard Zumkeller, Apr 06 2014 CROSSREFS 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 KEYWORD nonn AUTHOR George J. Schaeffer (gschaeff(AT)andrew.cmu.edu), Apr 29 2005 STATUS approved

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Last modified May 20 12:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)