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%I #41 Feb 11 2023 20:26:07
%S 0,1,3,6,7,8,16,21,22,36,42,55,76,108,123,140,144,156,172,240,259,312,
%T 366,384,504,531,568,656,810,924,1032,1056,1140,1260,1356,1698,2040,
%U 2088,2216,2520,2644,3108,3474,3480,4272,4572,4844,5280,5304,5412,6840
%N Records for sum of proper divisors function A001065.
%H Don Reble, <a href="/A034091/b034091.txt">Table of n, a(n) for n = 1..6524</a> (first 372 terms from _T. D. Noe_, terms 373 to 1000 from _Donovan Johnson_, terms 1001 to 2750 from Robert G. Wilson v)
%t With[{list1=DeleteDuplicates[Array[DivisorSigma[1, #]-#&, 3000, 0]]}, list2 = {}; Table[If[list1[[n]]>Max[list2], AppendTo[list2, list1[[n]]]], {n, Length[ list1]}]; list2] (* _Harvey P. Dale_, Dec 30 2011 *)
%t t = {0}; n = 1; mx = 0; While[Length[t] < 100, n++; s = DivisorSigma[1, n] - n; If[s > mx, mx = s; AppendTo[t, mx]]]; t (* _T. D. Noe_, Feb 23 2012 *)
%t DeleteDuplicates[Array[DivisorSigma[1,#]-#&,3000],GreaterEqual] (* _Harvey P. Dale_, Aug 20 2022 *)
%o (PARI) r=0; for(n=1,1e9, t=sigma(n)-n; if(t>r, r=t; print1(t", "))) \\ _Charles R Greathouse IV_, Feb 09 2017
%Y Cf. A001065, A034090.
%K nonn,nice
%O 1,3
%A _N. J. A. Sloane_, _J. Lowell_
%E More terms from _Erich Friedman_.