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A358546 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.

%I A358546 #41 Nov 22 2022 17:19:18
%S A358546 5480828320492525,4865,7735,455,131285,849355,11689795,286385,
%T A358546 187047685,104255,32851039955,2085985,47942199242945,189296520259,
%U A358546 349700961302721360788238344333849,580068028631,50392682631679406080371010751466781
%N A358546 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 A358546 If a(n) > -1 then a(n)*3^n is the least amicable number k such that A007949(k) = n.
%H A358546 BOINC, <a href="https://sech.me/boinc/Amicable/">Amicable Numbers</a>
%e A358546 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 A358546 (PARI)
%o A358546 sigmap(k)=if(k,sigma(k)-k,0)
%o A358546 cycle(k, TT=2)=my(x=k, T=1); while(x>0&&T<=TT, x=sigmap(x); if(x==k, return(T)); T++)
%o A358546 a(n, TT=2)=my(p3n=3^n); forstep(m=1, +oo, 2, if(m%3&&cycle(p3n*m, TT)==2, return(m)))
%Y A358546 Cf. A347770, A000396, A001065, A002025, A259180, A262625.
%Y A358546 Cf. A090748, A358415, A358320, A358022.
%K A358546 nonn,more
%O A358546 0,1
%A A358546 _Jean-Marc Rebert_, Nov 21 2022