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).
3, 2, 4, 20, 19, 7, 32, 21, 9, 54, 34, 11, 96, 42, 15, 132, 86, 18, 168, 60, 20, 217, 100, 22, 240, 114, 24, 252, 96, 23, 294, 164, 25, 338, 337, 27, 350, 349, 28, 464, 463, 31, 465, 200, 32, 582, 386, 35, 819, 288, 41, 1052, 1051, 48, 1080, 408, 47, 1182, 1181, 50
Offset: 1
Examples
The table begins:
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| row | u = | smallest k with | smallest m with |
| n | A352810(n) | A000203(k) = u | A024816(m) = u |
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n=1 : 3, 2, 4;
n=2 : 20, 19, 7;
n=3 : 32, 21, 9;
n=4 : 54, 34, 11;
n=5 : 96, 42, 15;
n=6 : 132, 86, 18;
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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.
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.
Programs
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Mathematica
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 *)
Extensions
More terms from Amiram Eldar, Apr 13 2022
Comments