A256440 Regular triangle where the n-th row lists the integers k between 1 and n ordered by increasing value of sigma(k)/k where sigma is the sum of divisors, A000203.

1, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 5, 3, 2, 4, 1, 5, 3, 2, 4, 6, 1, 7, 5, 3, 2, 4, 6, 1, 7, 5, 3, 2, 4, 8, 6, 1, 7, 5, 3, 9, 2, 4, 8, 6, 1, 7, 5, 3, 9, 2, 4, 10, 8, 6, 1, 11, 7, 5, 3, 9, 2, 4, 10, 8, 6, 1, 11, 7, 5, 3, 9, 2, 4, 10, 8, 6, 12, 1, 13, 11, 7, 5, 3, 9, 2, 4, 10, 8, 6, 12

Offset: 1

Author

Michel Marcus, Mar 29 2015

Keywords

• nonn
• tabl

Examples

			Triangle starts:
1;
1, 2;
1, 3, 2;
1, 3, 2, 4;
1, 5, 3, 2, 4;
1, 5, 3, 2, 4, 6;
1, 7, 5, 3, 2, 4, 6;
...
		

Links

• Michel Marcus, Rows n = 1..100 of triangle, flattened
• Michel Marcus, 100 rows

Crossrefs

Cf. A000203, A247015, A247022.

Programs

Mathematica

f[n_] := Block[{t = Table[0, {n}], j, k}, For[j = 1, j <= n, j++, t[[j]] = {}; For[k = 1, k <= j, k++, AppendTo[t[[j]], DivisorSigma[1, k]/k]]]; Ordering /@ t]; f@ 13 // Flatten (* Michael De Vlieger, Mar 29 2015 *)

PARI

lista(nn) = {for (n=1, nn, v = vector(n, k, sigma(k)/k); w = vecsort(v,,1); for (k=1, n, print1(w[k], ", ")); print(););}