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A071939
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a(n) = Max { sigma(k) : k = 1, 2, 3, ..., n } - Max { Phi(k) : k = 1, 2, 3, ..., n }.
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0
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0, 2, 2, 5, 3, 8, 6, 9, 9, 12, 8, 18, 16, 16, 16, 19, 15, 23, 21, 24, 24, 24, 20, 38, 38, 38, 38, 38, 32, 44, 42, 42, 42, 42, 42, 61, 55, 55, 55, 55, 51, 56, 54, 54, 54, 54, 50, 78, 78, 78, 78, 78, 72, 72, 72, 72, 72, 72, 66, 110, 108, 108, 108, 108, 108, 108, 102, 102, 102
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OFFSET
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1,2
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COMMENTS
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Is there a simple expression for lim_{n->oo} a(n)/n?
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LINKS
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FORMULA
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MATHEMATICA
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nn=70; With[{sig=DivisorSigma[1, Range[nn]], phi=EulerPhi[Range[ nn]]}, Table[ Max[Take[sig, n]]-Max[Take[phi, n]], {n, nn}]] (* Harvey P. Dale, May 06 2012 *)
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PROG
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(PARI) for(n=1, 100, v=vector(n, x, sigma(x)); w=vector(n, y, eulerphi(y)); print1(vecmax(v)-vecmax(w), ", "))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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