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

Author

T. D. Noe, Mar 28 2014

Keywords

• nonn
• tabf

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A238895.

Programs

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}]