A331580 Smallest number whose unsorted prime signature is the reversed unsorted prime signature of n.

1, 2, 2, 4, 2, 6, 2, 8, 4, 6, 2, 18, 2, 6, 6, 16, 2, 12, 2, 18, 6, 6, 2, 54, 4, 6, 8, 18, 2, 30, 2, 32, 6, 6, 6, 36, 2, 6, 6, 54, 2, 30, 2, 18, 18, 6, 2, 162, 4, 12, 6, 18, 2, 24, 6, 54, 6, 6, 2, 150, 2, 6, 18, 64, 6, 30, 2, 18, 6, 30, 2, 108, 2, 6, 12, 18, 6

Offset: 1

Author

Gus Wiseman, Apr 18 2020

Keywords

• nonn

Comments

Unsorted prime signature (A124010) is the sequence of exponents in a number's prime factorization.

Examples

			The prime signature of 12345678 = 2*3*3*47*14593 is (1,2,1,1), and the least number with prime signature (1,1,2,1) is 1050 = 2*3*5*5*7, so a(12345678) = 1050.
		

Crossrefs

The range is A055932.

The non-reversed version is A071364.

Unsorted prime signature is A124010.

Numbers whose prime signature is aperiodic are A329139.

Cf. A056239, A112798, A233249, A333217, A333219, A334032, A334033.

Programs

Mathematica

ptnToNorm[y_]:=Join@@Table[ConstantArray[i,y[[i]]],{i,Length[y]}];
Table[Times@@Prime/@ptnToNorm[Reverse[Last/@If[n==1,{},FactorInteger[n]]]],{n,100}]