|
%I
%S 20,25,43,44,49,59,122,206,2485,11899,17608,24141,56207,195236,
%T 2424613,2842925,6241233,59087970,111205290,124735931,224269761,
%U 1086241193
%N 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 44 works in both directions: n -> sigma(n) and sigma(n) -> n. See A269307.
%e 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 with(numtheory): P:=proc(q,h) local a,b,k,n,t,v; v:=array(1..h);
%p for n from 2 to q do a:=n; b:=ilog10(a)+1; if b>1 then
%p 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 while v[t]<sigma(n) do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p if v[t]=sigma(n) then print(n); fi; fi; od; end: P(10^6, 1000);
%t 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 Cf. A000203, A007629, A269307, A269309, A269310, A269311, A269312.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Feb 24 2016
%E a(16)-a(22) from _Lars Blomberg_, Jan 18 2018
|
