A247012 - OEIS

%I #27 Mar 19 2023 10:47:38

%S 6,133,172,841,1005,1603,4258,5299,192901,498906,1633303,5307589,

%T 16333303,20671542,41673714,42999958,73687923

%N 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.

%C A072234 is a subset of this sequence.

%C a(18) > 2*10^8. - _Tyler Busby_, Mar 19 2023

%e Aliquot parts of 1005 are 1, 3, 5, 15, 67, 201 and 335:

%e   1 + 3 + 5 + 15 + 67 + 201 + 335 = 627;

%e   3 + 5 + 15 + 67 + 201 + 335 + 627 = 1253;

%e   5 + 15 + 67 + 201 + 335 + 627 + 1253 = 2503;

%e   15 + 67 + 201 + 335 + 627 + 1253 + 2503 = 5001 that is the reverse of 1005.

%e Aliquot parts of 1603 are 1, 7 and 229:

%e   1 + 7 + 229 = 237;

%e   7 + 229 + 237 = 473;

%e   229 + 237 + 473 = 939;

%e   237 + 473 + 939 = 1649;

%e   473 + 939 + 1649 = 3061 that is the reverse of 1603;

%p with(numtheory): R:=proc(w) local x,y; x:=w; y:=0;

%p while x>0 do y:=10*y+(x mod 10); x:=trunc(x/10); od: y; end:

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

%p for n from 2 to q do if not isprime(n) then

%p a:=sort([op(divisors(n))]); b:=nops(a)-1; c:=ilog10(n)+1;

%p for k from 1 to b do v[k]:=a[k]; od;

%p t:=b+1; v[t]:=add(v[k], k=1..b);

%p if R(v[t])=n then print(n); else

%p while ilog10(v[t])+1<=c do t:=t+1; v[t]:=add(v[k], k=t-b..t-1);

%p if R(v[t])=n then print(n); break; fi; od; fi; fi; od;

%p end: P(10^9, 1000);

%t A247012 = {};

%t For[n = 4, n <= 1000000, n++,

%t  If[PrimeQ[n], Continue[]];

%t  r = IntegerReverse[n];

%t  a = Most[Divisors[n]];

%t  sum = Total[a];

%t  While[sum < r, sum = Total[a = Join[Rest[a], {sum}]]];

%t  If[sum == r, AppendTo[A247012, n]];

%t ]; A247012 (* _Robert Price_, Sep 08 2019 *)

%o (Python)

%o from sympy import isprime, divisors

%o A247012_list = []

%o for n in range(2,10**9):

%o ....m = int(str(n)[::-1])

%o ....if not isprime(n):

%o ........x = divisors(n)

%o ........x.pop()

%o ........y = sum(x)

%o ........while y < m:

%o ............x, y = x[1:]+[y], 2*y-x[0]

%o ........if y == m:

%o ............A247012_list.append(n) # _Chai Wah Wu_, Sep 12 2014

%Y Cf. A072234, A097090, A246544, A247013.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Sep 09 2014

%E a(9), a(11)-a(17) from _Chai Wah Wu_, Sep 13 2014