cp's OEIS Frontend

A352989 Composites k such that the k-th triangular number is divisible by the integer log of k.

%I A352989 #12 Apr 20 2022 00:07:57
%S A352989 8,15,16,27,44,54,72,84,90,95,105,125,143,150,180,195,231,256,264,287,
%T A352989 288,308,315,319,328,351,390,423,440,483,495,512,528,540,558,559,560,
%U A352989 576,588,608,624,627,645,648,650,728,800,805,819,840,855,870,884,896,897,924,935,945,960,975,987
%N A352989 Composites k such that the k-th triangular number is divisible by the integer log of k.
%C A352989 Composites k such that A000217(k) is divisible by A001414(k).
%C A352989 Contains all odd members of A046346, and in particular p^(p^k) if p is an odd prime and k >= 1.
%H A352989 Robert Israel, <a href="/A352989/b352989.txt">Table of n, a(n) for n = 1..10000</a>
%e A352989 a(5) = 44 = 2*2*11 is a term because it is composite and A000217(44) = 44*45/2 = 990 is divisible by 2+2+11 = 15.
%p A352989 filter:= proc(n) local t; not isprime(n) and (n*(n+1)/2/add(t[1]*t[2],t=ifactors(n)[2]))::integer end proc:
%p A352989 select(filter, [$4..1000]);
%t A352989 Select[Range[1000], CompositeQ[#] && Divisible[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]] &] (* _Amiram Eldar_, Apr 13 2022 *)
%Y A352989 Cf. A000217, A001414, A046346.
%K A352989 nonn
%O A352989 1,1
%A A352989 _J. M. Bergot_ and _Robert Israel_, Apr 13 2022