A284493 Analog of Keith numbers based on digits of sum of anti-divisors.

18, 26, 40, 93, 95, 122, 227, 5640, 8910, 15481, 56028, 117056, 282103, 394608, 2059983, 3775282, 3804607, 5005918, 10390740, 31753906, 42117745, 67170923, 98908536, 176337241

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..24.

Example

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

Maple

with(numtheory): P:=proc(q, h) local a, b, j, k, n, t, v; v:=array(1..h);
for n from 10^6 to q do k:=0; j:=n; while j mod 2 <> 1 do
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;
b:=ilog10(a)+1; if b>1 then for k from 1 to b do
v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1;
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;
if v[t]=n then print(n); fi; fi; od; end: P(10^9, 1000);

Crossrefs

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

Sequence in context: A212049 A212052 A093018 * A337523 A167336 A328687

Adjacent sequences: A284490 A284491 A284492 * A284494 A284495 A284496

Keyword

nonn,base,hard,more

Author

Paolo P. Lava, Mar 28 2017

Extensions

a(18)-a(24) from Georg Fischer, Oct 26 2019

Status

approved