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%I #15 Mar 29 2017 08:58:04
%S 1,19,23,213,211,293,2519,827,2129,2593,23259,2707,253653,21143,21927,
%T 21799,2177667,21529,8239969,25579,21757,232153,67719697,210229,
%U 2112597,2171101,217519,211879,27857904077,211007,25135138387,219059,2914689,4878977,4646637,230693
%N a(n) is the least number such that d(a(n)) = d(R(a(n)))/n, where R(n) is the digit reverse of n and d(n) is the number of divisors of n.
%F Solutions of the equation A000005(n) = A000005(A004086(n))/n.
%e d(1) = 1. Its digit reverse is again 1 and d(1) = 1 = 1 * 1;
%e d(19) = 2 and d(91) = 4 = 2 * 2;
%e d(23) = 2 and d(32) = 6 = 3 * 2;
%e d(213) = 4 and d(312) = 16 = 4 * 4; 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 2 to q do
%p if k*tau(n)=tau(R(n)) then print(n); break; fi; od; od; end: P(10^9);
%t rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; d[n_] := DivisorSigma[0, n]; a[n_] := Block[{k}, For[k=1, d@ rev@ k != n d@ k, k++]; k]; Array[a, 16] (* _Giovanni Resta_, Mar 29 2017 *)
%Y Cf. A000005, A004086, A284496 - A284498.
%K nonn,base
%O 1,2
%A _Paolo P. Lava_, Mar 28 2017
%E a(19)-a(36) from _Giovanni Resta_, Mar 29 2017
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