A239628 - OEIS

%I #7 Mar 31 2014 17:39:18

%S 1,9,2,6,4,12,8,16,48,144,32,96,64,192,128,256,768,2304,512,1536,1024,

%T 3072,2048,4096,12288,36864,8192,24576,16384,49152,32768,65536,196608,

%U 589824,131072,393216,262144,786432,524288,1048576,3145728,9437184,2097152

%N Factored over the Gaussian integers, the least positive number having n prime factors counted multiply, including units -1, i, and -i.

%C Here -1, i, and -i are counted as factors. The factor 1 is counted only in a(1). All these numbers of products of 2^k, 3, and 9.

%C Similar to A164073, which gives the least integer having n prime factors (over the Gaussian integers) shifted by 1.

%e a(2) = 9 because 9 = 3 * 3.

%e a(3) = 2 because 2 = -i * (1 + i)^2.

%e a(4) = 6 because 6 = -i * (1 + i)^2 * 3.

%t nn = 30; t = Table[0, {nn}]; n = 0; found = 0; While[found < nn, n++; cnt = Total[Transpose[FactorInteger[n, GaussianIntegers -> True]][[2]]]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = n; found++]]; t

%Y Cf. A001221, A001222 (integer factorizations).

%Y Cf. A078458, A086275 (Gaussian factorizations).

%Y Cf. A164073 (least number having n Gaussian factors, excluding units);

%Y Cf. A239627 (number of Gaussian factors of n, including units).

%Y Cf. A239629, A239630 (similar, but count distinct prime factors).

%K nonn

%O 1,2

%A _T. D. Noe_, Mar 31 2014