OFFSET
1,1
EXAMPLE
10*11/2 - sigma(10) = 55 - 18 = 37 and 3 + 7 = 10;
5217*5218/2 - sigma(5217) = 13611153 - 7296 = 13603857 and 1360 + 3857 = 5217.
MAPLE
with(numtheory): P:=proc(q) local a, b, c, i, n;
for n from 1 to q do c:=n*(n+1)/2-sigma(n); for i from 1 to ilog10(c) do
a:=trunc(c/10^i); b:=c-a*10^i; if a+b=n then print(n); break;
fi; od; od; end: P(10^9);
MATHEMATICA
Select[Range[10^5], Function[n, Total@ Boole@ Function[k, n == First@ # + Last@ # & /@ Map[FromDigits /@ TakeDrop[IntegerDigits@ k, #] &, Range[IntegerLength@ k - 1]]][n (n + 1)/2 - DivisorSigma[1, n]] > 0]] (* Michael De Vlieger, May 07 2016, Version 10.2 *)
ok[t_, n_] := Catch@ Block[{p=10}, While[p<t, If[n == Mod[t, p] + Floor[t/p], Throw@ True, p *= 10]]; False]; Select[ Range[10^5], ok[# (# + 1)/2 - DivisorSigma[1, #], #] &] (* Giovanni Resta, May 07 2016, older Mma, faster *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 06 2016
EXTENSIONS
a(15)-a(28) from Giovanni Resta, May 07 2016
STATUS
approved