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 A385748 #11 Jul 12 2025 18:50:26
%S A385748 1,2,6,8,12,24,32,54,96,108,128,192,216,240,384,486,512,864,972,1536,
%T A385748 1728,1944,2048,2160,3072,3456,4374,6000,6144,7776,8192,8748,13824,
%U A385748 15552,17496,19440,24576,27648,31104,32768,39366,49152,54000,55296,61440,65280,69984
%N A385748 Numbers k such that A384247(k) divides k.
%C A385748 (2^(2^k)-1) * 2^(2^k) is a term for k = 0..5.
%C A385748 Apparently, the only prime factors of any term are 2 and the Fermat primes (A019434), i.e., A092506.
%C A385748 Apparently, except for n = 1, a(n) / A384247(a(n)) is either 2 or 3.
%H A385748 Amiram Eldar, <a href="/A385748/b385748.txt">Table of n, a(n) for n = 1..250</a>
%e A385748 n | a(n) | a(n) / A384247(a(n))
%e A385748 --+------+---------------------
%e A385748 1 | 1 | 1 / 1 = 1
%e A385748 2 | 2 | 2 / 1 = 2
%e A385748 3 | 6 | 6 / 2 = 3
%e A385748 4 | 8 | 8 / 4 = 2
%e A385748 5 | 12 | 12 / 6 = 2
%t A385748 f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ f @@@ FactorInteger[n]; q[n_] := Divisible[n, iphi[n]]; Select[Range[70000], q]
%o A385748 (PARI) iphi(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i, 1]^(1 << valuation(f[i, 2], 2))));}
%o A385748 isok(k) = !( k % iphi(k));
%Y A385748 Cf. A019434, A092506, A384247.
%Y A385748 Similar sequences: A007694, A298759, A319481, A335327, A373057.
%K A385748 nonn
%O A385748 1,2
%A A385748 _Amiram Eldar_, Jul 08 2025