A076931 - OEIS

%I #10 Jul 19 2015 01:18:56

%S 1,1,3,2,125,2,16807,3,4,8,2357947691,5,1792160394037,32,135,24,

%T 2862423051509815793,10,5480386857784802185939,12,1701,512,

%U 39471584120695485887249589623,15,400,2048,972,48,3053134545970524535745336759489912159909

%N Smallest k such that n*k has n divisors.

%C n=p_1^a_1*...*p_r^a_r => tau(p_1^(p_1^a_1-1)*...*p_r^(p_r^a_r-1))=n, so sequence is well-defined.

%F a(p)=p^(p-2), a(pq)=p^(q-2)*q^(p-2) for p<q, a(2^2)=2, a(p^2)=p^(p-3)*2^(p-1) for p!=2.

%t f[n_] := Block[{k = 1, m = If[ PrimeQ[n], n^(n-2), 1]}, While[ DivisorSigma[0, k*m*n] != n, k++ ]; k*m]; Table[f[n], {n, 29}] (* _Robert G. Wilson v_, Sep 29 2005 *)

%Y a(n)= A073904(n)/n.

%K nonn

%O 1,3

%A _Amarnath Murthy_, Oct 18 2002

%E More terms from _Sascha Kurz_, Jan 21 2003

%E More terms from _David Wasserman_, Aug 19 2005