|
%I #14 Sep 02 2023 17:35:52
%S 1,2,4,6,12,24,30,60,120,180,210,360,420,840,1260,2520,4620,9240,
%T 13860,27720,55440,60060,120120,180180,360360,720720,1441440,1801800,
%U 2042040,3063060,6126120,12252240,24504480,30630600,36756720,38798760,58198140,116396280
%N Numbers k for which sigma(k^2)/k^2 reaches a new record, where sigma = A000203.
%C Appears to be almost identical to A308471.
%H MathOverflow, <a href="https://mathoverflow.net/questions/381843/on-superabundant-like-numbers">On superabundant-like numbers</a>
%e a(1) = 1 with sigma(1^2)/1^2 = 1.
%e a(2) = 2 with sigma(2^2)/2^2 = 7/4 > 1.
%e 3 is not in the sequence because sigma(3^2)/3^2 = 13/9 < 7/4.
%e a(3) = 4 with sigma(4^2)/4^2 = 31/16 > 7/4.
%p wmax:= 0: R:= NULL:
%p for n from 1 to 10^6 do
%p w:= numtheory:-sigma(n^2)/n^2;
%p if w > wmax then
%p wmax:= w; R:= R, n;
%p fi;
%p od:
%p R;
%t DeleteDuplicates[Table[{k,DivisorSigma[1,k^2]/k^2},{k,31*10^5}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* The program generates the first 30 terms of the sequence. To generate more increase the k constant (now set at 31*10^5) but the program may take a long time to run. *) (* _Harvey P. Dale_, Sep 02 2023 *)
%Y Cf. A000203, A004394, A308471.
%K nonn
%O 1,2
%A _Robert Israel_, Jan 22 2021
|
