cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A068992 Composite numbers k such that Sum_{d|k} sigma(d)/tau(d) is an integer.

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%I A068992 #15 Jun 08 2022 03:29:00
%S A068992 10,15,21,26,30,33,34,35,39,49,51,55,57,58,60,65,69,70,74,75,77,78,82,
%T A068992 85,87,91,93,95,98,102,105,106,110,111,115,119,120,122,123,129,130,
%U A068992 133,141,143,145,146,147,155,156,159,161,165,169,170,174,177,178,182,183
%N A068992 Composite numbers k such that Sum_{d|k} sigma(d)/tau(d) is an integer.
%C A068992 For p prime, contains p^2 if and only if p == 1 (mod 6). - _Robert Israel_, May 14 2019
%H A068992 Robert Israel, <a href="/A068992/b068992.txt">Table of n, a(n) for n = 1..10000</a>
%p A068992 N:= 1000:
%p A068992 V:= Vector(N):
%p A068992 for d from 1 to N do
%p A068992   r:= numtheory:-sigma(d)/numtheory:-tau(d);
%p A068992   C:= [seq(i,i=d..N,d)];
%p A068992   V[C]:= V[C] +~ r
%p A068992 od:
%p A068992 select(t -> not(isprime(t)) and V[t]::integer, [$2..N]); # _Robert Israel_, May 14 2019
%t A068992 q[n_] := CompositeQ[n] && IntegerQ @ DivisorSum[n, Divide @@ DivisorSigma[{1, 0}, #] &]; Select[Range[200], q] (* _Amiram Eldar_, Jun 08 2022 *)
%Y A068992 Contains A024556.
%Y A068992 Cf. A000005, A000203.
%K A068992 easy,nonn
%O A068992 1,1
%A A068992 _Benoit Cloitre_, Apr 06 2002