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 A369205 #14 Jul 29 2024 06:14:49
%S A369205 1,2,9,10,15,18,21,30,40,42,60,120,288,567,630,720,756,1023,1134,1428,
%T A369205 2046,2160,2268,2520,3024,3276,3570,4092,6048,8184,8925,9240,11424,
%U A369205 11550,15345,17850,18144,30690,35700,46200,57120,85680,147312,285600,491040,556920
%N A369205 Numbers m such that A188999(A034448(m)) = k*m for some k, where A034448 and A188999 are respectively the unitary and the bi-unitary sigma function.
%H A369205 Amiram Eldar, <a href="/A369205/b369205.txt">Table of n, a(n) for n = 1..105</a>
%e A369205 A034448(18) = 4 * 10 = 40 and A188999(40) = 15 * 6 = 90 = 5 * 18, so 18 is a term with k = 5.
%o A369205 (PARI) a034448(n) = {my(f,i,p,e);f=factor(n);for(i=1,#f~,p=f[i,1];e=f[i,2];f[i,1]=p^e+1;f[i,2]=1);factorback(f)};
%o A369205 a188999(n) = {my(f,i,p,e);f=factor(n);for(i=1,#f~,p=f[i,1];e=f[i,2];f[i,1]=if(e%2,(p^(e+1)-1)/(p-1),(p^(e+1)-1)/(p-1)-p^(e/2));f[i,2]=1);factorback(f)};
%o A369205 isok(n) = (a188999(a034448(n))%n) == 0;
%Y A369205 Cf. A038843 (analog for A034448(A034448(m))), A318175 (analog for A188999(A188999(m))).
%Y A369205 Cf. A369204 (analog for A034448(A188999(m))).
%K A369205 nonn
%O A369205 1,2
%A A369205 _Tomohiro Yamada_, Jan 16 2024