A284493 - OEIS

%I #15 Oct 27 2019 12:44:21

%S 18,26,40,93,95,122,227,5640,8910,15481,56028,117056,282103,394608,

%T 2059983,3775282,3804607,5005918,10390740,31753906,42117745,67170923,

%U 98908536,176337241

%N Analog of Keith numbers based on digits of sum of anti-divisors.

%C Consider the digits of the sum of anti-divisors of n. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.

%e Sum of the anti-divisors of 18 is 28: 2 + 8 = 10, 8 + 10 = 18.

%e Sum of the anti-divisors of 93 is 140: 1 + 4 + 0 = 5, 4 + 0 + 5 = 9, 0 + 5 + 9 = 14, 5 + 9 + 14 = 28, 9 + 14 + 28 = 51, 14 + 28 + 51 = 93.

%p with(numtheory): P:=proc(q,h) local a,b,j,k,n,t,v; v:=array(1..h);

%p for n from 10^6 to q do k:=0; j:=n; while j mod 2 <> 1 do

%p k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;

%p b:=ilog10(a)+1; if b>1 then for k from 1 to b do

%p v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1;

%p v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;

%p if v[t]=n then print(n); fi; fi; od; end: P(10^9, 1000);

%Y Cf. A066272, A282757 - A282765, A282766 - A282769.

%K nonn,base,hard,more

%O 1,1

%A _Paolo P. Lava_, Mar 28 2017

%E a(18)-a(24) from _Georg Fischer_, Oct 26 2019