login
Least odd number m such that m mod 3 > 0 and m*3^n is an amicable number, and -1 if no such number exists.
0

%I #41 Nov 22 2022 17:19:18

%S 5480828320492525,4865,7735,455,131285,849355,11689795,286385,

%T 187047685,104255,32851039955,2085985,47942199242945,189296520259,

%U 349700961302721360788238344333849,580068028631,50392682631679406080371010751466781

%N Least odd number m such that m mod 3 > 0 and m*3^n is an amicable number, and -1 if no such number exists.

%C If a(n) > -1 then a(n)*3^n is the least amicable number k such that A007949(k) = n.

%H BOINC, <a href="https://sech.me/boinc/Amicable/">Amicable Numbers</a>

%e a(1) = 4865, because 4865 is an odd number and 4865 % 3 > 0 and 4865 * 3 = 14595 is an amicable number, and no lesser number has this property.

%o (PARI)

%o sigmap(k)=if(k,sigma(k)-k,0)

%o cycle(k, TT=2)=my(x=k, T=1); while(x>0&&T<=TT, x=sigmap(x); if(x==k, return(T)); T++)

%o a(n, TT=2)=my(p3n=3^n); forstep(m=1, +oo, 2, if(m%3&&cycle(p3n*m, TT)==2, return(m)))

%Y Cf. A347770, A000396, A001065, A002025, A259180, A262625.

%Y Cf. A090748, A358415, A358320, A358022.

%K nonn,more

%O 0,1

%A _Jean-Marc Rebert_, Nov 21 2022