A324990 -id:A324990 - cp's OEIS frontend

A324991 a(n) = the largest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.

2, 4, 8, 12, 0, 18, 24, 21, 30, 36, 40, 48, 45, 60, 56, 72, 63, 84, 90, 75, 96, 120, 108, 112, 0, 144, 110, 140, 0, 180, 160, 156, 136, 67, 116, 210, 240, 200, 198, 252, 175, 224, 208, 225, 288, 228, 0, 360, 336, 0, 172, 315, 0, 330, 272, 420, 294, 306, 0, 396

Offset: 1

Jaroslav Krizek, Mar 23 2019

nonn

Floor(sigma(n)/tau(n)) = floor(A000203(n)/A000005(n)) = A057022(n) for n >= 1.

a(n) = 0 for numbers n = 5, 25, 29, 47, 50, 53, 59, 83, 89, ...

			For n = 4; number 12 is the largest number k with floor(sigma(k)/tau(k)) = 4; floor(sigma(12)/tau(12)) = floor(28/6) = 4.

Cf. A000005, A000203, A057022, A162538, A324990.

[Max([n: n in[1..10^5] | Floor(SumOfDivisors(n)/ NumberOfDivisors(n)) eq k]): k in [1..4]] cat [0] cat [Max([n: n in[1..10^5] | Floor(SumOfDivisors(n)/ NumberOfDivisors(n)) eq k]): k in [6..24]];

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

A324991 a(n) = the largest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.

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