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 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. 7
 6, 133, 172, 841, 1005, 1603, 4258, 5299, 192901, 498906, 1633303, 5307589, 16333303, 20671542, 41673714, 42999958, 73687923 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 1 18:30 EST 2024. Contains 370443 sequences. (Running on oeis4.)