%I #17 Jul 29 2020 03:45:31

%S 17,19,37,53,59,71,73,107,109,127,149,163,167,181,233,239,251,257,271,

%T 293,307,347,383,419,431,433,491,499,503,509,521,523,541,563,613,617,

%U 631,653,699,701,743,761,769,787,789,811,859,877,879,941,967

%N Numbers k such that twice the number of divisors of k is equal to the number of divisors of the sum of digits of k.

%C From _Robert Israel_, Jul 28 2020: (Start)

%C The first even term is a(2747)=68998.

%C Includes primes p such that A007953(p) is in A030513. (End)

%H Robert Israel, <a href="/A306510/b306510.txt">Table of n, a(n) for n = 1..10000</a>

%F 2*A000005(k) = A000005(A007953(k)).

%e For k = 19, 2*A000005(19) = A000005(A007953(19)), 2*A000005(19) = A000005(10), thus k = 19 is a member of the sequence.

%p filter:= proc(n) 2*numtheory:-tau(n) = numtheory:-tau(convert(convert(n,base,10),`+`)) end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Jul 28 2020

%o (PARI) isok(k) = (k >= 1) && (2*numdiv(k) == numdiv(sumdigits(k, 10))); \\ _Daniel Suteu_, Feb 20 2019

%Y Cf. A000005, A007953, A030513, A306509.

%K nonn,base

%O 1,1

%A _Ctibor O. Zizka_, Feb 20 2019