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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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 * A134468 A032611 A255200

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

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Last modified March 7 10:29 EST 2021. Contains 341869 sequences. (Running on oeis4.)