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A129902
Smallest multiple of n having exactly twice as many divisors as n.
7
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
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
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