|
%I #23 Nov 23 2023 16:24:33
%S 6,42,1430,3686,5685,23815,60235,129778,370991,652289,654545,660265,
%T 795405,801645,1532170,3413267,3457597,4235270,4282330,8107937,
%U 9679187,10835013,15464685,15963578,16636503,24976497,28122458,29595310,34759879,35642479,58525286
%N Squarefree composite numbers n such that n*sigma(n) is of the form k*(k+1).
%C Also squarefree composite numbers n such that Product_{p|n, p prime} A002378(p) is in A002378.
%C Is this sequence infinite?
%H Charles R Greathouse IV, <a href="/A291192/b291192.txt">Table of n, a(n) for n = 1..63</a>
%e 42 = 2*3*7 is a term because 42*sigma(42) = 42(2+1)(3+1)(7+1) = 4032 = 63*64.
%t Select[Range[586*10^5],CompositeQ[#]&&SquareFreeQ[#]&&OddQ[Sqrt[1+4(# DivisorSigma[ 1,#])]]&] (* _Harvey P. Dale_, Nov 23 2023 *)
%o (PARI) is(n,f=factor(n))=#f~>1 && vecmax(f[,2])==1 && ispolygonal(n*sigma(f)/2,3)
%o list(lim)=my(v=List()); forfactored(n=6,lim\1, if(call(is,n), listput(v,n[1]))); Vec(v) \\ _Charles R Greathouse IV_, Aug 22 2017
%Y Cf. A002378, A064987.
%K nonn
%O 1,1
%A _Altug Alkan_ and _Thomas Ordowski_, Aug 20 2017
|
