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.
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
Offset: 1
Keywords
Examples
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.
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
Programs
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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 *) -
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
Extensions
Terms beyond a(5) from Hans Havermann, Dec 02 2003