A284495 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.

1, 19, 23, 213, 211, 293, 2519, 827, 2129, 2593, 23259, 2707, 253653, 21143, 21927, 21799, 2177667, 21529, 8239969, 25579, 21757, 232153, 67719697, 210229, 2112597, 2171101, 217519, 211879, 27857904077, 211007, 25135138387, 219059, 2914689, 4878977, 4646637, 230693

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Formula

Solutions of the equation A000005(n) = A000005(A004086(n))/n.

Example

d(1) = 1. Its digit reverse is again 1 and d(1) = 1 = 1 * 1;
d(19) = 2 and d(91) = 4 = 2 * 2;
d(23) = 2 and d(32) = 6 = 3 * 2;
d(213) = 4 and d(312) = 16 = 4 * 4; etc.

Maple

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:=proc(q) local k, n; for k from 1 to q do for n from 2 to q do
if k*tau(n)=tau(R(n)) then print(n); break; fi; od; od; end: P(10^9);

Mathematica

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 *)

Crossrefs

Cf. A000005, A004086, A284496 - A284498.

Sequence in context: A107185 A240585 A226607 * A160077 A076353 A297575

Adjacent sequences: A284492 A284493 A284494 * A284496 A284497 A284498

Keyword

nonn,base

Author

Paolo P. Lava, Mar 28 2017

Extensions

a(19)-a(36) from Giovanni Resta, Mar 29 2017

Status

approved