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

Author

Paolo P. Lava, Feb 24 2016

Keywords

• nonn
• base
• more

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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]
				

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 *)

Extensions

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