%I #38 Aug 23 2022 14:39:20
%S 1,2,24,25,77,153,729,1183,1875,6174,7502,14819,15066,18225,19683,
%T 21384,26411,26624,28160,37179,146334,155000,157464,194579,236313,
%U 336091,399854,418950,632709,701519,818741,1572864,1605632,2001824,2067624,2142075,3670016,3746287
%N Numbers k >= 1 such that A000217(k) divided by A018804(k) is an integer.
%H Chai Wah Wu, <a href="/A349724/b349724.txt">Table of n, a(n) for n = 1..92</a>
%e k = 24: A000217(24) = 300, A018804(24) = 100, 300/100 = 3 thus 24 is a term.
%t A018804[n_]:=Apply[Times,Apply[((#1-1)#2/#1+1)#1^#2&,FactorInteger[n],{1}]]; (* After _Amiram Eldar_ in A018804 *)
%t upto=10^5;Reap[Do[If[Divisible[k(k+1)/2,A018804[k]],Sow[k]],{k,upto}]][[-1,-1]] (* _Paolo Xausa_, Aug 19 2022 *)
%o (PARI) isok(k) = !(k*(k+1)/2 % sumdiv(k, d, k*eulerphi(d)/d)); \\ _Michel Marcus_, Nov 27 2021
%o (Python)
%o from itertools import islice, count
%o from sympy import factorint
%o from math import prod
%o def A349724(): # generator of terms
%o for k in count(1):
%o if not k*(k+1)//2 % prod(p**(e-1)*((p-1)*e+p) for p, e in factorint(k).items()):
%o yield k
%o A349724_list = list(islice(A349724(),20)) # _Chai Wah Wu_, Nov 29 2021
%Y Cf. A000217, A018804.
%K nonn
%O 1,2
%A _Ctibor O. Zizka_, Nov 27 2021
%E a(12)-a(20) from _Paolo Xausa_, Nov 27 2021
%E More terms from _Amiram Eldar_, Nov 27 2021