A129902 Smallest multiple of n having exactly twice as many divisors as n.

2, 6, 6, 12, 10, 24, 14, 24, 18, 30, 22, 60, 26, 42, 30, 48, 34, 72, 38, 60, 42, 66, 46, 120, 50, 78, 54, 84, 58, 120, 62, 96, 66, 102, 70, 180, 74, 114, 78, 120, 82, 168, 86, 132, 90, 138, 94, 240, 98, 150, 102, 156, 106, 216, 110, 168, 114, 174, 118, 360, 122, 186, 126

Offset: 1

Author

J. Lowell, Jun 04 2007

Keywords

• nonn

Examples

			n=6 has 4 divisors. a(6) is not 12 or 18 because 12 and 18 have only 6 divisors as opposed to the 8 divisors required by the definition.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005.

Programs

Maple

A129902 := proc(n) local m; m := 2 ; while numtheory[tau](m*n)<> 2*numtheory[tau](n) do m := m+1 ; od ; RETURN(m*n) ; end: for n from 1 to 100 do printf("%d, ",A129902(n)) ; od ; # R. J. Mathar, Jun 07 2007

Mathematica

a[n_] := Module[{}, in = 2; While[Length[Divisors[in*n]] != 2*Length[Divisors[n]], in++ ]; in*n]; Table[a[i], {i, 1, 70}] (* Stefan Steinerberger, Jun 07 2007 *)

PARI

a(n) = {my(k=1); while (numdiv(n*k) != 2*numdiv(n), k++); n*k;} \\ Michel Marcus, Sep 15 2020

Formula

a(n) = {min(m*n): A000005(m*n)=2*A000005(n)}. - R. J. Mathar, Jun 07 2007

Extensions

Corrected and extended by R. J. Mathar, Stefan Steinerberger and Jon E. Schoenfield, Jun 07 2007