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

Author

Mohammed Yaseen, Jul 20 2022

Keywords

• nonn
• tabf

Examples

			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;
  ...
		

Crossrefs

Cf. A162538 (left border).

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

Programs

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 *)