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 A187941 #14 Mar 13 2023 09:55:27
%S A187941 1,2,4,8,12,32,24,128,48,72,96,2048,120,8192,384,288,240,131072,360,
%T A187941 524288,480,1152,6144,8388608,720,2592,24576,1800,1920,536870912,1440,
%U A187941 2147483648,1680,18432,393216,10368,2520,137438953472,1572864,73728,3360,2199023255552,5760,8796093022208
%N A187941 Least number with exactly n even divisors.
%C A187941 The only odd term in the sequence is 1, having zero even divisors. All larger odd numbers also have zero even divisors.
%C A187941 Conjecture: a(n) = 2^n only if n is prime or if n = 1.
%C A187941 If the prime factorization of a number is 2^k p1^e1...pr^er, then the number of even divisors is k*(e1+1)...(er+1). Hence, to find the least number having n even divisors, factor n and determine k, e1,..., er such that n = k*(e1+1)...(er+1). Then a(n) will have the form 2^k 3^e1 5^e2.... It is obvious that if n is prime, then a(n) = 2^n. Similarly, if n is twice an odd prime p, then a(n) = 2^p * 3. - _T. D. Noe_, Mar 16 2011
%F A187941 a(n) = 2 * A005179(n) for n > 0.
%t A187941 evenDivSigma[n_Integer] := Length[Select[Divisors[n], EvenQ]]; Flatten[Table[Take[Select[Range[2, 10^6, 2], evenDivSigma[#] == n &], 1], {n, 20}]] (* _Alonso del Arte_, Mar 16 2011 *)
%Y A187941 Cf. A000005, A005179, A038547, A183063.
%K A187941 nonn
%O A187941 0,2
%A A187941 _Juri-Stepan Gerasimov_, Mar 16 2011