%I #4 Dec 01 2022 17:29:07

%S 326,166,86,46,26,16,15,9,4,3,1,0

%N Aliquot sequence starting at 326.

%C Starting with untouchable number 326, this sequence is not a part of any larger aliquot sequence.

%C The sequence's pattern: 2^5*10+6, 2^4*10+6, 2^3*10+6, 2^2*10+6, 2^1*10+6, 2^0*10+6, 2^4-1, 2^3+1, 2^2-0, 2^1+1, 2^0-1.

%F a(n+1) = A001065(a(n)).

%F G.f.: 326 + 166*x + 86*x^2 + 46*x^3 + 26*x^4 + 16*x^5 + 15*x^6 + 9*x^7 + 4*x^8 + 3*x^9 + x^10.

%F E.g.f.: (1182988800 + 602380800*x + 156038400*x^2 + 27820800*x^3 + 3931200*x^4 + 483840*x^5 + 75600*x^6 + 6480*x^7 + 360*x^8 + 30*x^9 + x^10)/3628800.

%p with(numtheory): 326; while % > 0 do sigma(%)-% end do;

%t NestList[If[# == 0, 0, DivisorSigma[1, #] - #] &, 326, 11]

%o (PARI) x=326; print1(x ", "); while(x, x=sigma(x)-x; if(x, print1(x ", "), print1(x)))

%Y Includes A143759.

%K nonn,easy,fini,full

%O 0,1

%A _Michal Paulovic_, Oct 31 2022