cp's OEIS Frontend

A346113 Base-10 numbers k whose number of divisors equals the number of divisors in R(k), where k is written in all bases from base-2 to base-10 and R(k), the digit reversal of k, is read as a number in the same base.

%I A346113 #38 Jul 07 2021 07:18:05
%S A346113 1,9077,10523,10838,30182,58529,73273,77879,83893,244022,303253,
%T A346113 303449,304853,329893,332249,334001,334417,335939,336083,346741,
%U A346113 374617,391187,504199,512695,516982,595274,680354,687142,758077,780391,792214,854669,946217,948539,995761,1008487,1377067,1389341
%N A346113 Base-10 numbers k whose number of divisors equals the number of divisors in R(k), where k is written in all bases from base-2 to base-10 and R(k), the digit reversal of k, is read as a number in the same base.
%C A346113 There are 633 terms below 50 million and 1253 terms below 100 million. All of those have tau(k), the number of divisors of k, equal to 1, 2, 4, 8 or 16. The first term where tau(k) = 2 is n = 93836531, a prime, which is also the first term of A136634. All terms in A136634 will appear in this sequence, as will all terms in A228768(n) for n>=10. The first term with tau(k) = 4 is 9077, the first with tau(k) = 8 is 595274, and the first with tau(k) = 16 is 5170182. It is possible tau(k) must equal 2^i, with i>=0, although this is unknown.
%C A346113 All known terms are squarefree. - _Michel Marcus_, Jul 07 2021
%H A346113 Scott R. Shannon, <a href="/A346113/b346113.txt">Table of n, a(n) for n = 1..1253</a>
%e A346113 9077 is a term as the number of divisors of 9077 = tau(9077) = 4, and this equals the number of divisors of R(9077) when written and then read as a base-j number, with 2 <= j <= 10. See the table below for k = 9077.
%e A346113 .
%e A346113   base | k_base         | R(k_base)      | R(k_base)_10  | tau(R(k_base)_10)
%e A346113 ----------------------------------------------------------------------------------
%e A346113    2   | 10001101110101 | 10101110110001 | 11185         | 4
%e A346113    3   | 110110012      | 210011011      | 15421         | 4
%e A346113    4   | 2031311        | 1131302        | 6002          | 4
%e A346113    5   | 242302         | 203242         | 6697          | 4
%e A346113    6   | 110005         | 500011         | 38887         | 4
%e A346113    7   | 35315          | 51353          | 12533         | 4
%e A346113    8   | 21565          | 56512          | 23882         | 4
%e A346113    9   | 13405          | 50431          | 33157         | 4
%e A346113   10   | 9077           | 7709           | 7709          | 4
%t A346113 Select[Range@100000,Length@Union@DivisorSigma[0,Join[{s=#},FromDigits[Reverse@IntegerDigits[s,#],#]&/@Range[2,10]]]==1&] (* _Giorgos Kalogeropoulos_, Jul 06 2021 *)
%o A346113 (PARI) isok(k) = {my(t= numdiv(k)); for (b=2, 10, my(d=digits(k, b)); if (numdiv(fromdigits(Vecrev(d), b)) != t, return (0));); return(1);} \\ _Michel Marcus_, Jul 06 2021
%Y A346113 Cf. A000005, A004086.
%Y A346113 Cf. A030102, A030103, A030104, A030105, A030106, A030107, A030108.
%Y A346113 Cf. A136634 (prime terms), A228768.
%Y A346113 Subsequence of A062895.
%K A346113 nonn,base
%O A346113 1,2
%A A346113 _Scott R. Shannon_, Jul 05 2021