A269307 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.

17, 28, 31, 44, 51, 132, 133, 198, 208, 2528, 9241, 13570, 16577, 177568, 228742, 780889, 878078, 1854920, 2775787, 3663541, 8204010, 66326143, 73734437, 164211532, 670396359, 803230921, 832581731, 1036125551, 1572413223

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..29.

Example

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

Maple

with(numtheory): P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
for n from 2 to q do a:=sigma(n); b:=ilog10(a)+1; if b>1 then
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);
while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000);

Mathematica

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 *)

Crossrefs

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

Sequence in context: A217409 A256361 A293927 * A364555 A134468 A366963

Adjacent sequences: A269304 A269305 A269306 * A269308 A269309 A269310

Keyword

nonn,base,more

Author

Paolo P. Lava, Feb 24 2016

Extensions

a(20)-a(29) from Lars Blomberg, Jan 18 2018

Status

approved