A269307 - OEIS

%I #20 May 21 2019 22:07:07

%S 17,28,31,44,51,132,133,198,208,2528,9241,13570,16577,177568,228742,

%T 780889,878078,1854920,2775787,3663541,8204010,66326143,73734437,

%U 164211532,670396359,803230921,832581731,1036125551,1572413223

%N Consider the sum of the divisors of a number x>1. 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 x.

%C 44 works in both directions: sigma(n) -> n and n -> sigma(n). See A269308.

%e Sigma(17) = 18 :   1 + 8 = 9;  8 + 9 = 17.

%e Sigma(133) = 160 :  1 + 6 + 0 = 7;  6 + 0 + 7 = 13;  0 + 7 + 13 = 20; 7 + 13 + 20 = 40;  13 + 20 + 40 = 73;  20 + 40 + 73 = 133.

%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:=sigma(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]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;

%p if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000);

%t Select[Range[2,10^5], (t = #; d = IntegerDigits[DivisorSigma[1, #]]; While[Total[d] < t, d = Join[Rest[d], {Total[d]}]]; Total[d] == t) &] (* _Robert Price_, May 21 2019 *)

%Y Cf. A007629, A269308, A269309, A269310, A269311, A269312.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Feb 24 2016

%E a(20)-a(29) from _Lars Blomberg_, Jan 18 2018