A355848 Irregular triangle read by rows in which row n lists the numbers whose divisors have arithmetic mean n, or 0 if no such number exists.

1, 3, 5, 6, 7, 0, 11, 14, 15, 13, 20, 21, 17, 22, 30, 19, 27, 0, 23, 33, 35, 42, 45, 39, 44, 60, 29, 38, 54, 56, 31, 0, 46, 51, 55, 66, 70, 37, 49, 57, 41, 65, 68, 78, 96, 43, 0, 47, 62, 69, 77, 105, 0, 99, 126, 53, 85, 102, 110, 91, 92, 132, 140, 0, 59, 87, 95, 114, 135, 168

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Example

Triangle begins:
  n=1: 1;
  n=2: 3;
  n=3: 5, 6;
  n=4: 7;
  n=5: 0;
  n=6: 11, 14, 15;
  n=7: 13, 20;
  n=8: 21;
  n=9: 17, 22, 30;
  ...

Mathematica

nmax=30; a={}; For[n=1, n<=nmax, n++, nok=0; For[k=1, k<=n(n+1)/2, k++, If[DivisorSum[k, #&]==n*DivisorSigma[0, k], AppendTo[a, k]; nok=1]]; If[nok==0, AppendTo[a, 0]]]; a (* Stefano Spezia, Jul 20 2022 *)

Crossrefs

Cf. A162538 (left border).

Cf. A000005, A000203, A003601, A157847, A324990, A324991.

Sequence in context: A123572 A244953 A076819 * A181757 A181753 A082218

Adjacent sequences: A355845 A355846 A355847 * A355849 A355850 A355851

Keyword

nonn,tabf

Author

Mohammed Yaseen, Jul 20 2022

Status

approved