A157847 -id:A157847 - cp's OEIS frontend

A162538 The smallest number with an arithmetic mean of divisors equal to n; 0 if nonexistent.

1, 3, 5, 7, 0, 11, 13, 21, 17, 19, 0, 23, 45, 39, 29, 31, 0, 46, 37, 57, 41, 43, 0, 47, 0, 99, 53, 91, 0, 59, 61, 93, 86, 67, 116, 71, 73, 111, 125, 79, 0, 83, 0, 129, 89, 0, 0, 141, 97, 0, 101, 103, 0, 107, 109, 188, 113, 0, 0, 158, 169, 183, 166, 127, 261, 131, 0, 201, 137

Offset: 1

Claudio Meller, Jul 05 2009

nonn

a(n) is the smallest k such that sigma(k)/tau(k) = A000203(k)/A000005(k) = n.

Zeros occur if n is in A157847 (i.e., not in A157846).

			a(7)= 13 because sigma(13)=14 and tau(13)= 2 so 14/2 = 7.
a(8)= 21 because sigma(21)=32 and tau(21)= 4 so 32/4 = 8.

Cf. A003601.

Table[SelectFirst[Range[10^3],n*DivisorSigma[0,#]==DivisorSigma[1,#]&],{n,70}]/.(Missing["NotFound"]->0) (* Harvey P. Dale, Dec 14 2015 *)

Edited by R. J. Mathar, Aug 07 2009

A157846 Numbers which can be a mean of the divisors of some arithmetic number A003601(k).

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 45, 48, 49, 51, 52, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75

Offset: 1

Jaroslav Krizek, Mar 07 2009

nonn

This is A102187 sorted and duplicates removed.

Cf. A102187, A003601, A000203, A000005, A157847.

Edited by R. J. Mathar, Mar 15 2009

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.

Original entry on oeis.org

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

Mohammed Yaseen, Jul 20 2022

			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;
  ...

Cf. A162538 (left border).

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

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 *)

cp's OEIS Frontend

A162538 The smallest number with an arithmetic mean of divisors equal to n; 0 if nonexistent.

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A157846 Numbers which can be a mean of the divisors of some arithmetic number A003601(k).

Views

Author

Keywords

Comments

Crossrefs

Extensions

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.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica