cp's OEIS Frontend

A306510 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.

%I A306510 #17 Jul 29 2020 03:45:31
%S A306510 17,19,37,53,59,71,73,107,109,127,149,163,167,181,233,239,251,257,271,
%T A306510 293,307,347,383,419,431,433,491,499,503,509,521,523,541,563,613,617,
%U A306510 631,653,699,701,743,761,769,787,789,811,859,877,879,941,967
%N A306510 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 A306510 From _Robert Israel_, Jul 28 2020: (Start)
%C A306510 The first even term is a(2747)=68998.
%C A306510 Includes primes p such that A007953(p) is in A030513. (End)
%H A306510 Robert Israel, <a href="/A306510/b306510.txt">Table of n, a(n) for n = 1..10000</a>
%F A306510 2*A000005(k) = A000005(A007953(k)).
%e A306510 For k = 19, 2*A000005(19) = A000005(A007953(19)), 2*A000005(19) = A000005(10), thus k = 19 is a member of the sequence.
%p A306510 filter:= proc(n) 2*numtheory:-tau(n) = numtheory:-tau(convert(convert(n,base,10),`+`)) end proc:
%p A306510 select(filter, [$1..1000]); # _Robert Israel_, Jul 28 2020
%o A306510 (PARI) isok(k) = (k >= 1) && (2*numdiv(k) == numdiv(sumdigits(k, 10))); \\ _Daniel Suteu_, Feb 20 2019
%Y A306510 Cf. A000005, A007953, A030513, A306509.
%K A306510 nonn,base
%O A306510 1,1
%A A306510 _Ctibor O. Zizka_, Feb 20 2019