A324991 -id:A324991 - cp's OEIS frontend

A324990 a(n) = the smallest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.

1, 3, 5, 7, 0, 11, 13, 21, 17, 19, 40, 23, 34, 39, 29, 31, 63, 46, 37, 57, 41, 43, 76, 47, 0, 99, 53, 74, 0, 59, 61, 93, 86, 67, 116, 71, 73, 111, 125, 79, 175, 83, 171, 121, 89, 122, 0, 141, 97, 0, 101, 103, 0, 107, 109, 188, 113, 250, 0, 158, 169, 183, 166

Offset: 1

Jaroslav Krizek, Mar 23 2019

Floor(sigma(n)/tau(n)) = floor(A000203(n)/A000005(n)) = A057022(n) for n >= 1.
Odd primes are terms.
a(n) = 0 for numbers n =  5, 25, 29, 47, 50, 53, 59, 83, 89, ...

			For n = 4; number 7 is the smallest number k with floor(sigma(k)/tau(k)) = 4; floor(sigma(7)/tau(7)) = floor(8/2) = 4.

Robert Israel, Table of n, a(n) for n = 1..2000

Cf. A000005, A000203, A057022, A162538, A324991.

Magma
```
Ax:=func; [Ax(n): n in[1..80]]
```

N:= 100: # for a(1)..a(N)
V:= Vector(N):
for k from 1 to N^2 do
  v:= floor(numtheory:-sigma(k)/numtheory:-tau(k));
  if v <= N and V[v]=0 then V[v]:= k fi
od:
convert(V,list); # Robert Israel, Sep 13 2020

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

A324990 a(n) = the smallest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.

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