A186444 The count of numbers <= n for which 3 is an infinitary divisor.

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, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19

Offset: 1

Author

Vladimir Shevelev, Feb 21 2011

Keywords

• nonn

Comments

For the definition of infinitary divisors, see A037445.

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A123087, A037445.

Partial sums of A182581.

Programs

Maple

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

Formula

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

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

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