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.
%I A068997 #49 Apr 19 2025 04:04:24
%S A068997 1,2,4,6,8,12,16,18,20,24,32,36,40,48,54,64,72,80,84,96,100,108,120,
%T A068997 128,144,160,162,168,192,200,216,240,252,256,272,288,312,320,324,336,
%U A068997 360,384,400,432,440,480,486,500,504,512,544,576,588,600,624,640,648
%N A068997 Numbers k such that Sum_{d|k} d*mu(d) divides k.
%C A068997 Numbers k such that A023900(k) divides k.
%C A068997 The only squarefree terms so far are a(1), a(2), and a(4). - _Torlach Rush_, Dec 04 2017
%C A068997 There are no more squarefree terms. The squarefree terms are also the squarefree terms of A007694 since A023900(n) = A008683(n) * A000010(n) for squarefree numbers n, and A007694 contains only 3-smooth numbers (A003586). - _Amiram Eldar_, Apr 19 2025
%C A068997 There is a surjective mapping from all even numbers not in this sequence to terms of the sequence. The first such is 10 to a(9). The next is 14, 28, 42 to a(19). All even numbers not in the sequence are divisors of some term in the sequence. - _Torlach Rush_, Dec 08 2017
%H A068997 Amiram Eldar, <a href="/A068997/b068997.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%p A068997 with(numtheory): A068997 := i->`if`(i mod phi(mul(j,j=factorset(i)))=0,i,NULL): seq(A068997(i),i=1..650); # _Peter Luschny_, Nov 02 2010
%t A068997 Select[Range[650], Divisible[#, DivisorSum[#, # MoebiusMu[#] &]] &] (* _Michael De Vlieger_, Nov 20 2017 *)
%t A068997 q[1] =True; q[n_] := Divisible[n, Times @@ ((First[#] - 1) & /@ FactorInteger[n])]; Select[Range[650], q] (* _Amiram Eldar_, Apr 19 2025 *)
%o A068997 (PARI) for(n=1,1000,if(n%sumdiv(n,d,moebius(d)*d)==0,print1(n,",")))
%o A068997 (PARI) isok(k) = !(k % vecprod(apply(x -> 1-x, factor(k)[, 1]))); \\ _Amiram Eldar_, Apr 19 2025
%o A068997 (Haskell)
%o A068997 a068997 n = a068997_list !! (n - 1)
%o A068997 a068997_list = filter (\x -> mod x (a173557 x) == 0) [1..]
%o A068997 -- _Reinhard Zumkeller_, Jun 01 2015
%Y A068997 Cf. A000010, A003586, A007694, A008683, A023900, A173557, A293928.
%K A068997 easy,nonn
%O A068997 1,2
%A A068997 _Benoit Cloitre_, Apr 07 2002