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

1,2

Comments

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

Links

Table of n, a(n) for n=1..77.

Example

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.

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}]

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.

Sequence in context: A067824 A347458 A107067 * A320389 A046801 A348717

Adjacent sequences: A331577 A331578 A331579 * A331581 A331582 A331583

Keyword

nonn

Author

Gus Wiseman, Apr 18 2020

Status

approved