The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A106315

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A106315

Harmonic residue of n.
(history; published version)

#11 by Harvey P. Dale at Thu Feb 29 15:15:47 EST 2024

STATUS

editing

approved

#10 by Harvey P. Dale at Thu Feb 29 15:15:43 EST 2024

MATHEMATICA

HarmonicResidue[n_]=Mod[n*DivisorSigma[0, n], DivisorSigma[1, n]]; HarmonicResidue[ Range[ 80]]

EXTENSIONS

Mathematica program completed by Harvey P. Dale, Feb 29 2024

STATUS

approved

editing

#9 by R. J. Mathar at Wed Jan 25 05:49:01 EST 2017

STATUS

editing

approved

#8 by R. J. Mathar at Wed Jan 25 05:48:46 EST 2017

COMMENTS

a(n) = A038040(n) - A000203(n) * A240471(n) . - Reinhard Zumkeller, Apr 06 2014

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

CROSSREFS

Cf. A106316, A106317, A001599 (positions of zeros).

STATUS

approved

editing

#7 by Reinhard Zumkeller at Sun Apr 06 15:37:14 EDT 2014

STATUS

editing

approved

#6 by Reinhard Zumkeller at Sun Apr 06 14:46:55 EDT 2014

COMMENTS

a(n) = A038040(n) - A000203(n) * A240471(n) . - Reinhard Zumkeller, Apr 06 2014

PROG

(Haskell)

a106315 n = n * a000005 n `mod` a000203 n -- Reinhard Zumkeller, Apr 06 2014

CROSSREFS

Cf. A000005, A000203.

#5 by Reinhard Zumkeller at Sun Apr 06 14:45:13 EDT 2014

LINKS

Reinhard Zumkeller, <a href="/A106315/b106315.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

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.

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

CROSSREFS

Cf. 106316, 106317A106316, A106317.

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

HarmonicResidue[n_]=Mod[n*DivisorSigma[0, n], DivisorSigma[1, n]]

KEYWORD

nonn,new

nonn