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%I #11 Feb 29 2024 15:15:47
%S 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,
%T 28,0,28,24,30,3,36,28,44,51,36,32,44,50,40,48,42,12,36,40,46,108,33,
%U 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
%N Harmonic residue of n.
%C 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.
%H Reinhard Zumkeller, <a href="/A106315/b106315.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A038040(n) - A000203(n) * A240471(n) . - _Reinhard Zumkeller_, Apr 06 2014
%p A106315 := proc(n)
%p modp(n*numtheory[tau](n),numtheory[sigma](n)) ;
%p end proc:
%p seq(A106315(n),n=1..100) ; # _R. J. Mathar_, Jan 25 2017
%t HarmonicResidue[n_]=Mod[n*DivisorSigma[0, n], DivisorSigma[1, n]]; HarmonicResidue[ Range[ 80]]
%o (Haskell)
%o a106315 n = n * a000005 n `mod` a000203 n -- _Reinhard Zumkeller_, Apr 06 2014
%Y Cf. A106316, A106317, A001599 (positions of zeros).
%Y Cf. A000005, A000203.
%K nonn
%O 1,3
%A George J. Schaeffer (gschaeff(AT)andrew.cmu.edu), Apr 29 2005
%E Mathematica program completed by _Harvey P. Dale_, Feb 29 2024
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