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.

%I A324990 #9 Sep 08 2022 08:46:24
%S A324990 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,
%T A324990 99,53,74,0,59,61,93,86,67,116,71,73,111,125,79,175,83,171,121,89,122,
%U A324990 0,141,97,0,101,103,0,107,109,188,113,250,0,158,169,183,166
%N A324990 a(n) = the smallest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.
%C A324990 Floor(sigma(n)/tau(n)) = floor(A000203(n)/A000005(n)) = A057022(n) for n >= 1.
%C A324990 Odd primes are terms.
%C A324990 a(n) = 0 for numbers n =  5, 25, 29, 47, 50, 53, 59, 83, 89, ...
%H A324990 Robert Israel, <a href="/A324990/b324990.txt">Table of n, a(n) for n = 1..2000</a>
%e A324990 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.
%p A324990 N:= 100: # for a(1)..a(N)
%p A324990 V:= Vector(N):
%p A324990 for k from 1 to N^2 do
%p A324990   v:= floor(numtheory:-sigma(k)/numtheory:-tau(k));
%p A324990   if v <= N and V[v]=0 then V[v]:= k fi
%p A324990 od:
%p A324990 convert(V,list); # _Robert Israel_, Sep 13 2020
%o A324990 (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]]
%Y A324990 Cf. A000005, A000203, A057022, A162538, A324991.
%K A324990 nonn,look
%O A324990 1,2
%A A324990 _Jaroslav Krizek_, Mar 23 2019