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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000005.

Sequence in context: A062562 A208570 A106832 * A350631 A087560 A071892

Adjacent sequences: A129899 A129900 A129901 * A129903 A129904 A129905

Keyword

nonn

Author

J. Lowell, Jun 04 2007

Extensions

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

Status

approved