%I #12 Apr 20 2022 00:07:57

%S 8,15,16,27,44,54,72,84,90,95,105,125,143,150,180,195,231,256,264,287,

%T 288,308,315,319,328,351,390,423,440,483,495,512,528,540,558,559,560,

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

%C Composites k such that A000217(k) is divisible by A001414(k).

%C Contains all odd members of A046346, and in particular p^(p^k) if p is an odd prime and k >= 1.

%H Robert Israel, <a href="/A352989/b352989.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 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 select(filter, [$4..1000]);

%t Select[Range[1000], CompositeQ[#] && Divisible[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]] &] (* _Amiram Eldar_, Apr 13 2022 *)

%Y Cf. A000217, A001414, A046346.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 13 2022