OFFSET
1,1
COMMENTS
44 works in both directions: sigma(n) -> n and n -> sigma(n). See A269308.
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
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Feb 24 2016
EXTENSIONS
a(20)-a(29) from Lars Blomberg, Jan 18 2018
STATUS
approved