A247012 Consider the aliquot parts, in ascending order, of a composite number. Take their sum and repeat the process deleting the minimum number and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to the reverse of themselves.

6, 133, 172, 841, 1005, 1603, 4258, 5299, 192901, 498906, 1633303, 5307589, 16333303, 20671542, 41673714, 42999958, 73687923

Offset

1,1

Comments

A072234 is a subset of this sequence.

a(18) > 2*10^8. - Tyler Busby, Mar 19 2023

Links

Table of n, a(n) for n=1..17.

Example

Aliquot parts of 1005 are 1, 3, 5, 15, 67, 201 and 335:
  1 + 3 + 5 + 15 + 67 + 201 + 335 = 627;
  3 + 5 + 15 + 67 + 201 + 335 + 627 = 1253;
  5 + 15 + 67 + 201 + 335 + 627 + 1253 = 2503;
  15 + 67 + 201 + 335 + 627 + 1253 + 2503 = 5001 that is the reverse of 1005.
Aliquot parts of 1603 are 1, 7 and 229:
  1 + 7 + 229 = 237;
  7 + 229 + 237 = 473;
  229 + 237 + 473 = 939;
  237 + 473 + 939 = 1649;
  473 + 939 + 1649 = 3061 that is the reverse of 1603;

Maple

with(numtheory): R:=proc(w) local x, y; x:=w; y:=0;
while x>0 do y:=10*y+(x mod 10); x:=trunc(x/10); od: y; end:
P:=proc(q, h) local a, b, c, k, n, t, v; v:=array(1..h);
for n from 2 to q do if not isprime(n) then
a:=sort([op(divisors(n))]); b:=nops(a)-1; c:=ilog10(n)+1;
for k from 1 to b do v[k]:=a[k]; od;
t:=b+1; v[t]:=add(v[k], k=1..b);
if R(v[t])=n then print(n); else
while ilog10(v[t])+1<=c do t:=t+1; v[t]:=add(v[k], k=t-b..t-1);
if R(v[t])=n then print(n); break; fi; od; fi; fi; od;
end: P(10^9, 1000);

Mathematica

A247012 = {};
For[n = 4, n <= 1000000, n++,
 If[PrimeQ[n], Continue[]];
 r = IntegerReverse[n];
 a = Most[Divisors[n]];
 sum = Total[a];
 While[sum < r, sum = Total[a = Join[Rest[a], {sum}]]];
 If[sum == r, AppendTo[A247012, n]];
]; A247012 (* Robert Price, Sep 08 2019 *)

Prog

(Python)
from sympy import isprime, divisors
A247012_list = []
for n in range(2, 10**9):
....m = int(str(n)[::-1])
....if not isprime(n):
........x = divisors(n)
........x.pop()
........y = sum(x)
........while y < m:
............x, y = x[1:]+[y], 2*y-x[0]
........if y == m:
............A247012_list.append(n) # Chai Wah Wu, Sep 12 2014

Crossrefs

Cf. A072234, A097090, A246544, A247013.

Sequence in context: A152289 A015503 A350611 * A003373 A129047 A209276

Adjacent sequences: A247009 A247010 A247011 * A247013 A247014 A247015

Keyword

nonn,base,more

Author

Paolo P. Lava, Sep 09 2014

Extensions

a(9), a(11)-a(17) from Chai Wah Wu, Sep 13 2014

Status

approved