A186444 - OEIS

%I #18 Jun 25 2022 00:40:51

%S 0,0,1,1,1,2,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,

%T 9,9,9,9,10,10,10,11,11,11,11,11,11,12,12,12,13,13,13,14,14,14,15,15,

%U 15,16,16,16,16,16,16,17,17,17,18,18,18,18,18,18,19

%N The count of numbers <= n for which 3 is an infinitary divisor.

%C For the definition of infinitary divisors, see A037445.

%C The sequence is the partial sums of the characteristic function of the numbers with 3 as one of the infinitary divisors; these are 3, 6, 12, 15, 21, 24, 27, 30 etc, apparently shown in A145204. - _R. J. Mathar_, Feb 28 2011

%H Amiram Eldar, <a href="/A186444/b186444.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(n/3) - a(floor(n/3)).

%F a(n) = floor(n/3) - floor(n/9) + floor(n/27) - ....

%F a(n) grows as n/4 as n tends to infinity.

%p A186444 := proc(n) local a,k ; option remember; if n< 3 then 0; else floor(n/3) -procname(floor(n/3)) ; end if; end proc: # _R. J. Mathar_, Feb 28 2011

%Y Cf. A123087, A037445.

%Y Partial sums of A182581.

%K nonn

%O 1,6

%A _Vladimir Shevelev_, Feb 21 2011