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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..60.

Example

The table begins:
  ------------------------------------------------------------------
  | row |      u =        | smallest k with  |    smallest m with  |
  |  n  |   A352810(n)    |  A000203(k) = u  |     A024816(m) = u  |
  ------------------------------------------------------------------
    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;
  ...................................................................
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.

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 *)

Crossrefs

Cf. A000203, A002191, A024816, A076617, A231365, A352810.

Sequence in context: A185390 A361422 A369776 * A019116 A213611 A355776

Adjacent sequences: A352808 A352809 A352810 * A352812 A352813 A352814

Keyword

nonn,tabf

Author

Bernard Schott, Apr 12 2022

Extensions

More terms from Amiram Eldar, Apr 13 2022

Status

approved