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