A255243 Number x such that x | A255242(x).

1, 4, 10, 16, 18, 64, 80, 96, 195, 256, 462, 576, 768, 880, 1024, 2560, 3120, 3136, 4096, 6656, 16384, 40704, 53248, 57344, 64000, 65536, 67896, 78864, 80640, 101376, 103680, 120320, 120336, 125440, 126208, 139264, 147968, 195840, 217600, 225280, 250624, 262144

Offset: 1

Author

Paolo P. Lava, Feb 19 2015

Keywords

• nonn

Comments

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

Examples

			For a(1) = 1 we have sigma(1) - 1 = 0 and 0 / 1 = 0.
Aliquot parts of a(2) = 4 are 1, 2 and their sum is 3.
Let us repeat the calculation with 1 and 2: 1 => 0; 2 => 1.
Their sum is 1. Finally, 3 + 1 = 4 and 4 / 4 = 1.
Aliquot parts of a(3) = 10 are 1, 2, 5. Their sum is 8.
Let us repeat the calculation with 1, 2 and 5: 1 => 0; 2 => 1; 5 => 1.
Their sum is 2. Finally, 8 + 2 = 10 and 10 / 10 = 1.
Aliquot parts of a(4) = 16 are 1, 2, 4, 8. Their sum is 15.
Let us repeat the calculation with 1, 2, 4 and 8: 1 => 0; 2 => 1; 4 => 1, 2; 8 => 1, 2, 4.
Their sum is 1 + 1 + 2 + 1 + 2 + 4 = 11.
Repeat the calculation with 1, 1, 2, 1, 2, 4: 1 => 0; 1 => 0; 2 => 1; 1 => 0; 2 => 1;  4 => 1, 2.
Their sum is 1 + 1 + 1 + 2 = 5.
Repeat the calculation with 1, 1, 1, 2: 1 => 0; 1 => 0; 1 => 0; 2 => 1; Their sum is 1.
Finally, 15 + 11 + 5 + 1 = 32 and 32 / 16 = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A001065, A255242.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,c,k,n,t,v;
for n from 1 to q do b:=0; a:=sort([op(divisors(n))]); t:=nops(a)-1;
while add(a[k],k=1..t)>0 do b:=b+add(a[k],k=1..t); v:=[];
for k from 2 to t do c:=sort([op(divisors(a[k]))]); v:=[op(v),op(c[1..nops(c)-1])]; od;
a:=v; t:=nops(a); od; if type(b/n,integer) then print(n); fi; od; end: P(10^9);

Mathematica

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

Extensions

a(32)-a(42) from Amiram Eldar, Apr 06 2019