A281879 Non-palindromic numbers k such that sigma(k) | sigma(R(k)), where R(k) is the digit reversal of k.

15, 16, 17, 59, 129, 165, 176, 187, 205, 273, 276, 299, 429, 446, 478, 528, 599, 825, 1034, 1043, 1135, 1209, 1239, 1515, 1561, 1565, 1616, 1651, 1665, 1717, 1776, 1887, 2086, 2165, 2178, 2255, 2455, 2515, 2618, 2739, 2829, 3489, 4008, 4064, 4475, 4604, 5346, 5795

Offset: 1

Author

Paolo P. Lava, Feb 01 2017

Keywords

• nonn
• easy
• base

Examples

			a(1) = 15 because sigma(51) / sigma(15) = 72 / 24 = 3;
a(2) = 16 because sigma(61) / sigma(16) = 62 / 31 = 2;
a(3) = 17 because sigma(71) / sigma(17) = 72 / 18 = 4.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500
• Paolo P. Lava, First 250 terms with the ratio sigma(R(k))/sigma(k)

Crossrefs

Cf. A000203, A004086, A085329, A281880.

Programs

Maple

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local n; for n from 1 to q do
if n<>T(n) then if type(sigma(T(n))/sigma(n),integer) then print(n); fi; fi; od; end: P(10^6);

Mathematica

Select[Range[6000],!PalindromeQ[#]&&Mod[DivisorSigma[1,IntegerReverse[#]],DivisorSigma[ 1,#]] ==0&] (* Harvey P. Dale, Dec 19 2023 *)