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 A089044 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 320. LINKS 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 EXAMPLE 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. MATHEMATICA 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 *) PROG (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

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)