A300447 Numbers x such that sigma(x) = sigma(y), with x<>y, where y is the 10's complement mod 10 of the digits of x.

54, 56, 513, 520, 546, 564, 580, 597, 4845, 5130, 5223, 5454, 5656, 5887, 5970, 6265, 44226, 46365, 48450, 50260, 50840, 51300, 52230, 52520, 53768, 57342, 58580, 58870, 59700, 62650, 64745, 66884, 463650, 477972, 484500, 489132, 489632, 493752, 501536, 503274

Offset: 1

Author

Paolo P. Lava, Mar 06 2018

Keywords

• nonn
• base
• easy

Examples

			sigma(54) = sigma(56) = 120;
sigma(513) = sigma(597) = 800;
sigma(477972) = sigma(633138) = 1415232.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A000203, A055120.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,n;
for n from 1 to q do a:=convert(n,base,10);
for k from 1 to nops(a) do a[k]:=(10-a[k]) mod 10; od; b:=0;
for k from 1 to nops(a) do b:=b*10+a[nops(a)-k+1]; od;
if b<>n and sigma(b)=sigma(n) then print(n); fi; od; end: P(10^6);

Mathematica

Select[Range[10^6], Apply[And[#1 != #2, DivisorSigma[1, #1] == DivisorSigma[1, #2]] &, {#, FromDigits[IntegerDigits[#] /. d_?Positive :> 10 - d]}] &] (* Michael De Vlieger, Mar 09 2018 *)

PARI

isok(x) = {my(dx = digits(x), dy = vector(#dx, k, (10-dx[k]) % 10), y = fromdigits(dy)); (x != y) && (sigma(x) == sigma(y));} \\ Michel Marcus, Mar 07 2018