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 A340230 #25 Feb 27 2021 22:12:11 %S A340230 1,1,193,613,1124581,52071301,213536830501 %N A340230 a(n) is the smallest number m such that numbers m, m + 1, m + 2, ..., m + n - 1 have k, 2*k, 4*k, 8*k, ..., (2^(n-1))*k divisors respectively. %C A340230 a(n) is the smallest number m such that tau(m) = tau(m + 1) / 2 = tau(m + 2) / 4 = tau(m + 3) / 8 = ... = tau(m + n - 1) / 2^(n - 1), where tau(k) = the number of divisors of k (A000005). %C A340230 Conjecture: a(7) = 213536830501. %e A340230 a(4) = 613 because 613 is the smallest term of 4 consecutive numbers with this property: tau(613) = 2, tau(614) = 4, tau(615) = 8, tau(616) = 16. %o A340230 (PARI) isok(m, n) = my(nb=numdiv(m)); for (k=1, n-1, if (numdiv(m+k)/nb != 2^k, return(0))); return (1); %o A340230 a(n) = my(k=1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Jan 05 2021 %Y A340230 Cf. A100366 (similar sequence for primes). %Y A340230 Cf. A000005, A063446, A100363, A100364, A100365, A340229. %K A340230 nonn,more %O A340230 1,3 %A A340230 _Jaroslav Krizek_, Jan 01 2021 %E A340230 a(7), as conjectured by Jaroslav Krizek, from _Martin Ehrenstein_, Feb 06 2021