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A352811 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).

%I A352811 #29 Apr 18 2022 22:44:58
%S A352811 3,2,4,20,19,7,32,21,9,54,34,11,96,42,15,132,86,18,168,60,20,217,100,
%T A352811 22,240,114,24,252,96,23,294,164,25,338,337,27,350,349,28,464,463,31,
%U A352811 465,200,32,582,386,35,819,288,41,1052,1051,48,1080,408,47,1182,1181,50
%N A352811 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 A352811 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 A352811 The table begins:
%e A352811   ------------------------------------------------------------------
%e A352811   | row |      u =        | smallest k with  |    smallest m with  |
%e A352811   |  n  |   A352810(n)    |  A000203(k) = u  |     A024816(m) = u  |
%e A352811   ------------------------------------------------------------------
%e A352811     n=1 :         3,                   2,                   4;
%e A352811     n=2 :        20,                  19,                   7;
%e A352811     n=3 :        32,                  21,                   9;
%e A352811     n=4 :        54,                  34,                  11;
%e A352811     n=5 :        96,                  42,                  15;
%e A352811     n=6 :       132,                  86,                  18;
%e A352811   ...................................................................
%e A352811 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 A352811 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 A352811 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 A352811 Cf. A000203, A002191, A024816, A076617, A231365, A352810.
%K A352811 nonn,tabf
%O A352811 1,1
%A A352811 _Bernard Schott_, Apr 12 2022
%E A352811 More terms from _Amiram Eldar_, Apr 13 2022