%I #29 Apr 18 2022 22:44:58
%S 3,2,4,20,19,7,32,21,9,54,34,11,96,42,15,132,86,18,168,60,20,217,100,
%T 22,240,114,24,252,96,23,294,164,25,338,337,27,350,349,28,464,463,31,
%U 465,200,32,582,386,35,819,288,41,1052,1051,48,1080,408,47,1182,1181,50
%N Table read by rows: row n gives triples (u, k, m) such that k and m are the smallest integers that respectively satisfy A352810(n) = u = A000203(k) = A024816(m).
%C A000203 is the function sigma sum of divisors, while A024816 is the antisigma function, sum of the numbers less than n that do not divide n.
%e The table begins:
%e ------------------------------------------------------------------
%e | row | u = | smallest k with | smallest m with |
%e | n | A352810(n) | A000203(k) = u | A024816(m) = u |
%e ------------------------------------------------------------------
%e n=1 : 3, 2, 4;
%e n=2 : 20, 19, 7;
%e n=3 : 32, 21, 9;
%e n=4 : 54, 34, 11;
%e n=5 : 96, 42, 15;
%e n=6 : 132, 86, 18;
%e ...................................................................
%e 3rd row is (32, 21, 9) because A352810(3) = 32, sigma(21) = sigma(31) = 32 and antisigma(9) = 2+4+5+6+7+8 = 32, hence 21 and 9 are respectively the smallest integers k and m such that sigma(k) = antisigma(m) = 32.
%e 5th row is (96, 42, 15) because A352810(5) = 96 and 42 and 15 are respectively the smallest integers k and m such that sigma(k) = antisigma(m) = 96.
%t m = 2000; r = Range[m]; s = DivisorSigma[1, r]; as = r*(r + 1)/2 - s; i = Select[Intersection[s, as], # <= m &]; Flatten @ Transpose @ Join[{i}, Map[Flatten[Table[FirstPosition[#, i[[k]]], {k, 1, Length[i]}]] &, {s, as}]] (* _Amiram Eldar_, Apr 12 2022 *)
%Y Cf. A000203, A002191, A024816, A076617, A231365, A352810.
%K nonn,tabf
%O 1,1
%A _Bernard Schott_, Apr 12 2022
%E More terms from _Amiram Eldar_, Apr 13 2022