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A279088 Numbers k for which sigma(k) - 3k exceeds sigma(j) - 3j for all j < k.

%I A279088 #29 Aug 27 2019 09:50:42
%S A279088 1,120,180,240,360,720,840,1260,1440,1680,2160,2520,3360,3780,3960,
%T A279088 4200,4680,5040,7560,9240,10080,12600,13860,15120,18480,20160,22680,
%U A279088 25200,27720,30240,32760,36960,37800,40320,42840,45360,50400,55440,65520,75600,83160
%N A279088 Numbers k for which sigma(k) - 3k exceeds sigma(j) - 3j for all j < k.
%C A279088 Positions of record lows in A033885. - _Robert Israel_, Jan 30 2017
%H A279088 Amiram Eldar, <a href="/A279088/b279088.txt">Table of n, a(n) for n = 1..350</a> (terms 1..125 from Robert Israel)
%e A279088 240 is in the sequence because sigma(240) - 3*240 = 744 - 720 = 24, and no k < 240 has a value of sigma(k) - 3k this large.
%p A279088 m:= numtheory:-sigma(1) - 3:
%p A279088 count:= 1:
%p A279088 A[1]:= 1:
%p A279088 for n from 2 to 10^6 do
%p A279088   v:= numtheory:-sigma(n)-3*n;
%p A279088   if v > m then
%p A279088      count:= count+1;
%p A279088      A[count]:= n;
%p A279088      m:= v;
%p A279088   fi;
%p A279088 od:
%p A279088 seq(A[i],i=1..count); # _Robert Israel_, Jan 30 2017
%t A279088 With[{s = Array[DivisorSigma[1, #] - 3 # &, 10^5]}, FirstPosition[s, #][[1]] & /@ Union@ FoldList[Max, s]] (* _Michael De Vlieger_, Dec 16 2017 *)
%o A279088 (PARI) isok(k) = {my(x = sigma(k) - 3*k); for (j=1, k-1, if (sigma(j) - 3*j > x, return (0));); 1;} \\ _Michel Marcus_, Jan 30 2017
%o A279088 (MATLAB)
%o A279088 N = 10^6; % to get all terms <= N
%o A279088 V = 1-3*[1:N];
%o A279088 m = V(1);
%o A279088 A(1) = 1;
%o A279088 for n=2:N
%o A279088   V(n*[1:N/n]) = V(n*[1:N/n]) + n;
%o A279088   if V(n) > m
%o A279088     m = V(n);
%o A279088     A(end+1) = n;
%o A279088   end
%o A279088 end
%o A279088 A % _Robert Israel_, Jan 30 2017
%Y A279088 Cf. A002093 (d=0), A034090 (d=1), and A140522 (d=2).
%Y A279088 Cf. A033885.
%K A279088 nonn
%O A279088 1,2
%A A279088 _Jon E. Schoenfield_, Jan 29 2017
%E A279088 Duplicate a(2)-a(43) removed from b-file by _Andrew Howroyd_, Feb 27 2018