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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000203, A004086, A211223.

Sequence in context: A345476 A217006 A053083 * A039435 A043258 A044038

Adjacent sequences: A246484 A246485 A246486 * A246488 A246489 A246490

Keyword

nonn,base,easy

Author

Paolo P. Lava, Aug 27 2014

Status

approved