A255243 - OEIS

%I #38 Apr 29 2019 20:50:01

%S 1,4,10,16,18,64,80,96,195,256,462,576,768,880,1024,2560,3120,3136,

%T 4096,6656,16384,40704,53248,57344,64000,65536,67896,78864,80640,

%U 101376,103680,120320,120336,125440,126208,139264,147968,195840,217600,225280,250624,262144

%N Number x such that x | A255242(x).

%C For 4, 10, 195 we have x = A255242(x).

%H Amiram Eldar, <a href="/A255243/b255243.txt">Table of n, a(n) for n = 1..50</a>

%e For a(1) = 1 we have sigma(1) - 1 = 0 and 0 / 1 = 0.

%e Aliquot parts of a(2) = 4 are 1, 2 and their sum is 3.

%e Let us repeat the calculation with 1 and 2: 1 => 0; 2 => 1.

%e Their sum is 1. Finally, 3 + 1 = 4 and 4 / 4 = 1.

%e Aliquot parts of a(3) = 10 are 1, 2, 5. Their sum is 8.

%e Let us repeat the calculation with 1, 2 and 5: 1 => 0; 2 => 1; 5 => 1.

%e Their sum is 2. Finally, 8 + 2 = 10 and 10 / 10 = 1.

%e Aliquot parts of a(4) = 16 are 1, 2, 4, 8. Their sum is 15.

%e Let us repeat the calculation with 1, 2, 4 and 8: 1 => 0; 2 => 1; 4 => 1, 2; 8 => 1, 2, 4.

%e Their sum is 1 + 1 + 2 + 1 + 2 + 4 = 11.

%e Repeat the calculation with 1, 1, 2, 1, 2, 4: 1 => 0; 1 => 0; 2 => 1; 1 => 0; 2 => 1;  4 => 1, 2.

%e Their sum is 1 + 1 + 1 + 2 = 5.

%e Repeat the calculation with 1, 1, 1, 2: 1 => 0; 1 => 0; 1 => 0; 2 => 1; Their sum is 1.

%e Finally, 15 + 11 + 5 + 1 = 32 and 32 / 16 = 2.

%p with(numtheory): P:=proc(q) local a,b,c,k,n,t,v;

%p for n from 1 to q do b:=0; a:=sort([op(divisors(n))]); t:=nops(a)-1;

%p while add(a[k],k=1..t)>0 do b:=b+add(a[k],k=1..t); v:=[];

%p for k from 2 to t do c:=sort([op(divisors(a[k]))]); v:=[op(v),op(c[1..nops(c)-1])]; od;

%p a:=v; t:=nops(a); od; if type(b/n,integer) then print(n); fi; od; end: P(10^9);

%t f[s_] := Flatten[Most[Divisors[#]] & /@ s]; a[n_] := Total@Flatten[FixedPointList[ f, {n}]] - n; Select[Range[10000], Divisible[a[#], #] &] (* _Amiram Eldar_, Apr 06 2019 *)

%Y Cf. A001065, A255242.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Feb 19 2015

%E a(32)-a(42) from _Amiram Eldar_, Apr 06 2019