A239625 Irregular triangle of numbers k that have A238895(n) as the sum of the proper divisors of each k.

4, 6, 25, 18, 51, 91, 32, 125, 161, 209, 221, 75, 215, 287, 407, 527, 551, 98, 175, 335, 671, 767, 1007, 1247, 1271, 581, 869, 1241, 1349, 1541, 1769, 1829, 1961, 2021, 545, 749, 1133, 1313, 1649, 2573, 2993, 3053, 3149, 3233, 243, 791, 1199, 1391, 1751, 1919

Offset

2,1

Comments

It is interesting that these numbers have a very simple factorization. For example, the terms in row 6 factor as 3*5^2, 5*43, 7*41, 11*37, 17*31, and 19*29.

Links

T. D. Noe, Rows n = 2..51 of irregular triangle, flattened

Example

The rows are
1: {empty}
2: 4,
3: 6, 25,
4: 18, 51, 91,
5: 32, 125, 161, 209, 221,
6: 75, 215, 287, 407, 527, 551,
7: 98, 175, 335, 671, 767, 1007, 1247, 1271,
8: 581, 869, 1241, 1349, 1541, 1769, 1829, 1961, 2021

Mathematica

nn = 200; s = Table[0, {nn}]; d = Table[DivisorSigma[1, n] - n, {n, (nn/2)^2}]; Do[If[0 < d[[n]] <= nn, s[[d[[n]]]]++], {n, (nn/2)^2}]; t = {}; mx = -1; Do[If[s[[n]] > mx, mx = s[[n]]; AppendTo[t, {n, mx}]], {n, 2, nn}]; t2 = Transpose[t][[1]]; Table[Flatten[Position[d, n]], {n, t2}]

Crossrefs

Cf. A238895.

Sequence in context: A136591 A277997 A009459 * A123055 A272306 A294996

Adjacent sequences: A239622 A239623 A239624 * A239626 A239627 A239628

Keyword

nonn,tabf

Author

T. D. Noe, Mar 28 2014

Status

approved