A284498 - OEIS

%I #16 Mar 29 2017 08:58:55

%S 1,16,15,17,2178,299,129,110959,116509,1001159

%N a(n) is the least number such that sigma(a(n)) = sigma(R(a(n)))/n, where R(n) is the digit reverse of n and sigma(n) is the sum of the divisors of n.

%C a(11) > 10^9. - _Giovanni Resta_, Mar 29 2017

%F Solutions of the equation A000203(n) = A000203(A004086(n))/n.

%e sigma(1) = 1. Its digit reverse is again 1 and sigma(1) = 1 = 1 * 1;

%e sigma(16) = 31 and sigma(61) = 62 = 2 * 31;

%e sigma(15) = 24 and sigma(51) = 72 = 3 * 24;

%e sigma(17) = 18 and sigma(71) = 72 = 4 * 18; etc.

%p with(numtheory): R:=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 P:=proc(q) local k,n; for k from 1 to q do for n from 1 to q do

%p if k*sigma(n)=sigma(R(n)) then print(n); break; fi; od; od; end: P(10^9);

%t rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; s[n_] := DivisorSigma[1, n]; a[n_] := Block[{k, v}, For[k = 1, Mod[v = s@rev@k, n] > 0 || v != n s@k, k++]; k]; Array[a, 10] (* _Giovanni Resta_, Mar 29 2017 *)

%Y Cf. A000203, A004086, A284495 - A284497.

%K nonn,more,base

%O 1,2

%A _Paolo P. Lava_, Mar 28 2017