|
%I #18 Sep 15 2020 10:12:43
%S 2,6,6,12,10,24,14,24,18,30,22,60,26,42,30,48,34,72,38,60,42,66,46,
%T 120,50,78,54,84,58,120,62,96,66,102,70,180,74,114,78,120,82,168,86,
%U 132,90,138,94,240,98,150,102,156,106,216,110,168,114,174,118,360,122,186,126
%N Smallest multiple of n having exactly twice as many divisors as n.
%H Ivan Neretin, <a href="/A129902/b129902.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = {min(m*n): A000005(m*n)=2*A000005(n)}. - _R. J. Mathar_, Jun 07 2007
%e 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.
%p 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
%t 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 *)
%o (PARI) a(n) = {my(k=1); while (numdiv(n*k) != 2*numdiv(n), k++); n*k;} \\ _Michel Marcus_, Sep 15 2020
%Y Cf. A000005.
%K nonn
%O 1,1
%A _J. Lowell_, Jun 04 2007
%E Corrected and extended by _R. J. Mathar_, _Stefan Steinerberger_ and _Jon E. Schoenfield_, Jun 07 2007
|
