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

1,2

Comments

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, ...

Links

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

Example

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.

Maple

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

Prog

(Magma) Ax:=func<n|exists(r){m:m in[1..10000] | Floor(SumOfDivisors(m)/ NumberOfDivisors(m)) eq n}select r else 0>; [Ax(n): n in[1..80]]

Crossrefs

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

Sequence in context: A085090 A084713 A162538 * A084712 A371144 A031100

Adjacent sequences: A324987 A324988 A324989 * A324991 A324992 A324993

Keyword

nonn,look

Author

Jaroslav Krizek, Mar 23 2019

Status

approved