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 A181808 #7 Feb 16 2025 08:33:13 %S A181808 2,4,8,12,24,48,72,96,120,240,360,480,720,1440,1680,2520,3360,5040, %T A181808 10080,15120,20160,30240,40320,50400,55440,90720,100800,110880,166320, %U A181808 221760,332640,443520,554400,665280,997920,1108800,1330560,1441440,2162160,2882880,4324320 %N A181808 Numbers that set a record for number of even divisors: a(n) = 2*A002182(n). %C A181808 In other words, a positive integer n appears in the sequence iff more even numbers divide n than divide any positive integer smaller than n. %C A181808 For all positive integer values (j,k) such that jk = n, the number of divisors of n that are multiples of j equals A000005(k). Therefore, n sets a record for the number of its divisors that are multiples of j iff k=n/j is highly composite (A002182). Cf. A181803, A181809, A181810. %H A181808 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a> %F A181808 a(n)=2*A002182(n). %e A181808 a(4)=12 has exactly four even divisors (2, 4, 6 and 12). (Note that these are precisely the numbers that are twice a divisor of A002182(4)=6; see row 6 of A027750.) No positive integer smaller than 12 has as many as four even divisors; hence, 12 is a member of the sequence. %Y A181808 Numbers n such that 2 appears in row n of A181803. See also A181809, A181810. %Y A181808 A002183(n) gives number of even divisors of a(n). %Y A181808 A053624 gives numbers that set records for number of odd divisors. No number sets records both for its number of odd divisors and its number of even divisors. %K A181808 nonn %O A181808 1,1 %A A181808 _Matthew Vandermast_, Nov 27 2010