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A269308 Consider a number x. Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach the sum of the divisors of x.

%I A269308 #20 May 21 2019 22:07:13
%S A269308 20,25,43,44,49,59,122,206,2485,11899,17608,24141,56207,195236,
%T A269308 2424613,2842925,6241233,59087970,111205290,124735931,224269761,
%U A269308 1086241193
%N A269308 Consider a number x. Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach the sum of the divisors of x.
%C A269308 44 works in both directions: n -> sigma(n) and sigma(n) -> n. See A269307.
%e A269308 sigma(20) = 42 :  2 + 0 = 2; 0 + 2 = 2; 2 + 2 = 4; 2 + 4 = 6; 4 + 6 = 10; 6 + 10 = 16; 10 + 16 = 26; 16 +26 = 42.
%p A269308 with(numtheory): P:=proc(q,h) local a,b,k,n,t,v; v:=array(1..h);
%p A269308 for n from 2 to q do a:=n; b:=ilog10(a)+1; if b>1 then
%p A269308 for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
%p A269308 while v[t]<sigma(n) do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A269308 if v[t]=sigma(n) then print(n); fi; fi; od; end: P(10^6, 1000);
%t A269308 Select[Range[10,10^5], (s = DivisorSigma[1, #]; d = IntegerDigits[#]; While[Total[d] < s, d = Join[Rest[d], {Total[d]}]]; Total[d] == s) &] (* _Robert Price_, May 21 2019 *)
%Y A269308 Cf. A000203, A007629, A269307, A269309, A269310, A269311, A269312.
%K A269308 nonn,base,more
%O A269308 1,1
%A A269308 _Paolo P. Lava_, Feb 24 2016
%E A269308 a(16)-a(22) from _Lars Blomberg_, Jan 18 2018