OFFSET
1,1
COMMENTS
44 works in both directions: n -> sigma(n) and sigma(n) -> n. See A269307.
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
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Feb 24 2016
EXTENSIONS
a(16)-a(22) from Lars Blomberg, Jan 18 2018
STATUS
approved