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 A309263 #25 Aug 03 2019 15:11:48
%S A309263 1,2,4,8,16,20,32,64,100,128,256,272,500,512,1024,2048,2500,4096,4624,
%T A309263 8192,10100,12500,16384,32768,62500,65536,65792,78608,131072,262144,
%U A309263 312500,524288,1020100,1048576,1336336,1562500,2097152,4194304,7812500,8388608
%N A309263 Terms of A140110 that are not divisible by 6.
%C A309263 Includes all powers of 2.
%C A309263 Conjecture: The sequence includes all numbers of the form 4*5^n.
%C A309263 The number 10100 is a counterexample for: (a) Prime factorizations of numbers of this sequence will always have only 2's and Fermat primes. (b) No number in this sequence is divisible by more than one distinct odd prime.
%e A309263 20 is in this sequence because it is in A140110 and is not divisible by 6.
%e A309263 24, which is in A140110, is not in this sequence because it is divisible by 6.
%o A309263 (PARI) isok(n) = {if(n%6 == 0, return(0)); my(d = divisors(n)); for (k=1, #d - 1, r = d[k+1]/d[k]; if(numerator(r) != denominator(r) + 1, return(0)); ); return(1); } \\ _Jinyuan Wang_, Aug 03 2019
%Y A309263 Cf. A140110, A000079, A005054.
%K A309263 nonn
%O A309263 1,2
%A A309263 _J. Lowell_, Jul 19 2019