A246487 Numbers x such that sigma(x) + sigma(R(x)) = sigma(x + R(x)), where R(x) is the digit reversal of x and sigma(x) is the sum of the divisors of x.

78, 87, 104, 401, 1144, 2072, 2178, 2702, 4411, 7038, 7348, 7878, 8307, 8437, 8712, 8787, 11144, 11544, 12584, 15834, 20710, 20913, 21476, 21978, 22164, 26070, 31902, 43851, 44111, 44511, 46122, 48521, 66649, 67412, 87912, 94666, 102786, 122584, 122784, 126984

Offset: 1

Author

Paolo P. Lava, Aug 27 2014

Keywords

• nonn
• base
• easy

Examples

			x = 15834 -> R(x) = 43851 and sigma(15834) + sigma(43851) = 40320 + 59904 = 100224 = sigma(15834 + 43851)= sigma(59685).
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000203, A004086, A211223.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,n;
for n from 1 to q do a:=n; b:=0;
for k from 1 to ilog10(n)+1 do b:=10*b+(a mod 10); a:=trunc(a/10);
od; if sigma(n)+sigma(b)=sigma(n+b) then print(n); fi;
od; end: P(10^6);

Mathematica

Select[Range[130000],DivisorSigma[1,#]+DivisorSigma[1,IntegerReverse[#]] == DivisorSigma[1,#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 27 2017 *)

PARI

isok(n) = rn = subst(Polrev(digits(n)), x, 10); sigma(n + rn) == sigma(n) + sigma(rn); \\ Michel Marcus, Aug 29 2014