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.

5480828320492525, 4865, 7735, 455, 131285, 849355, 11689795, 286385, 187047685, 104255, 32851039955, 2085985, 47942199242945, 189296520259, 349700961302721360788238344333849, 580068028631, 50392682631679406080371010751466781

Offset: 0

Author

Jean-Marc Rebert, Nov 21 2022

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Links

• BOINC, Amicable Numbers

Crossrefs

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

Cf. A090748, A358415, A358320, A358022.

Programs

PARI

sigmap(k)=if(k,sigma(k)-k,0)
cycle(k, TT=2)=my(x=k, T=1); while(x>0&&T<=TT, x=sigmap(x); if(x==k, return(T)); T++)
a(n, TT=2)=my(p3n=3^n); forstep(m=1, +oo, 2, if(m%3&&cycle(p3n*m, TT)==2, return(m)))