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 A338611 #4 Nov 04 2020 17:11:51
%S A338611 1,3,9,15,45,135,765,2295,196605,589815,12884901885,38654705655
%N A338611 Numbers all of whose divisors, excluding the divisor 1, are evil numbers (A001969) with a record number of divisors.
%C A338611 A number m is in this sequence if it is in A093688, and d(m) > d(k) for all terms k < m in A093688, where d(m) is the number of divisors of m (A000005).
%C A338611 The corresponding record numbers of divisors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, ...
%C A338611 Apparently, all the terms except for 1 are products of powers of Fermat primes (A019434). 3 seems to be the only prime with multiplicity larger than 1 in some of the terms. There are no other terms in this sequence that are products of powers of the 5 known Fermat primes.
%e A338611 The first 4 terms of A093688 are 1, 3, 5, 9, and their numbers of divisors are 1, 2, 2, 3. The record values 1, 2 and 3 occur at 1, 3 and 9 that are the first 3 terms of this sequence.
%t A338611 evilQ[n_] := EvenQ @ DigitCount[n, 2, 1]; allDivEvilQ[n_] := AllTrue[Rest @ Divisors[n], evilQ]; divNumMax = 0; seq={}; Do[If[allDivEvilQ[n] && (divNum = DivisorSigma[0, n]) > divNumMax, divNumMax = divNum; AppendTo[seq, n]], {n, 1, 6*10^5}]; seq
%Y A338611 Subsequence of A001969 and A093688.
%Y A338611 Similar sequence with odious numbers: A330289.
%Y A338611 Cf. A000005, A019434.
%K A338611 nonn,base,more
%O A338611 1,2
%A A338611 _Amiram Eldar_, Nov 03 2020