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A089044
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Numbers n such that abs(d(n) - log(n) + 1 - 2*gamma) is a decreasing sequence, where d(n) is the number of divisors A000005(n) and gamma is Euler's constant A001620.
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2
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1, 3, 5, 7, 46, 2514, 2522, 2526, 2534, 2536, 2542, 2546, 2553, 2555, 18873, 139454, 139475, 7614005, 7614010, 7614015, 7614022, 7614030, 7614033, 7614034, 7614056, 7614062, 7614066, 7614069, 7614079, 7614082, 7614086, 7614087, 7614088
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OFFSET
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1,2
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 320.
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LINKS
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Hugo Pfoertner, Table of n, a(n) for n = 1..7613
Leroy Quet, Two number-theoretical limits (& bonus sum). Thread in NG sci.math, Oct 30 2003.
Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant
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EXAMPLE
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a(5)=46 because d(46) - log(46) + 1 - 2*0.5772156649... = 0.016927274... is less than
abs(d(7) - log(7) + 1 - 2*0.5772156649...) = abs(-0.100341479...) with d(46)=4 and d(7)=2.
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MATHEMATICA
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f[n_] := N[ Abs[ DivisorSigma[0, n] - Log@ n + 1 - 2 EulerGamma], 32]; k = 1; lst = {}; mx = Infinity; While[k < 8000000, a = f@k; If[a < mx, mx = a; AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Dec 11 2017 *)
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PROG
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(PARI)
d=1.0; n=0; \
for(j=2, 16, kmin=round(exp(j-2*Euler+1-2*d)); kmax=round(exp(j-2*Euler+1+2*d)); \
for(k=kmin, kmax, dd=abs(numdiv(k)-log(k)+1-2*Euler); \
if(dd<d, d=dd; print1(k, ", "))))
\\ Hugo Pfoertner, Dec 08 2017
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CROSSREFS
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Cf. A000005 = number of divisors of n, A001620 = Euler's constant gamma, A089084.
Sequence in context: A261511 A146972 A102742 * A117646 A064857 A065913
Adjacent sequences: A089041 A089042 A089043 * A089045 A089046 A089047
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet and Hugo Pfoertner, Dec 02 2003
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EXTENSIONS
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Terms beyond a(5) from Hans Havermann, Dec 02 2003
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STATUS
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approved
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