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Search: id:A094471
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| 0, 1, 2, 5, 4, 12, 6, 17, 14, 22, 10, 44, 12, 32, 36, 49, 16, 69, 18, 78, 52, 52, 22, 132, 44, 62, 68, 112, 28, 168, 30, 129, 84, 82, 92, 233, 36, 92, 100, 230, 40, 240, 42, 180, 192, 112, 46, 356, 90, 207, 132, 214, 52, 312, 148, 328, 148, 142, 58, 552, 60, 152, 274, 321
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = SUM (n-d) where d is a divisor of n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 31 2005
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REFERENCES
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P. A. MacMahon, Combinatory Analysis, Cambridge Univ. Press, London and New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 30.
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FORMULA
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Row sums of triangle A134866 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 14 2007
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EXAMPLE
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If n is prime, then n.tau[n]-sigma[n]=2n-(n+1)=n-1=phi[n].
If n>1, then a[n]>0.
Not all values arise and some arise more than once.
q^2 + 2*q^3 + 5*q^4 + 4*q^5 + 12*q^6 + 6*q^7 + 17*q^8 + 14*q^9 + ...
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MATHEMATICA
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Table[w*DivisorSigma[0, w]-DivisorSigma[1, w], {w, 1, 100}]
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PROGRAM
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(PARI) {a(n) = if( n<1, 0, n * numdiv(n) - sigma(n))} /* Michael Somos Jan 25 2008 */
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CROSSREFS
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Cf. A000005, A000010, A000203.
Cf. A134866.
Sequence in context: A010078 A074639 A002314 this_sequence A126356 A121274 A111681
Adjacent sequences: A094468 A094469 A094470 this_sequence A094472 A094473 A094474
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 28 2004
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