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.

20, 25, 43, 44, 49, 59, 122, 206, 2485, 11899, 17608, 24141, 56207, 195236, 2424613, 2842925, 6241233, 59087970, 111205290, 124735931, 224269761, 1086241193

Offset

1,1

Comments

44 works in both directions: n -> sigma(n) and sigma(n) -> n. See A269307.

Links

Table of n, a(n) for n=1..22.

Example

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.

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:=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]<sigma(n) do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=sigma(n) then print(n); fi; fi; od; end: P(10^6, 1000);

Mathematica

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 *)

Crossrefs

Cf. A000203, A007629, A269307, A269309, A269310, A269311, A269312.

Sequence in context: A070684 A295152 A292199 * A167306 A061840 A252660

Adjacent sequences: A269305 A269306 A269307 * A269309 A269310 A269311

Keyword

nonn,base,more

Author

Paolo P. Lava, Feb 24 2016

Extensions

a(16)-a(22) from Lars Blomberg, Jan 18 2018

Status

approved