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A301461 Number of integers less than or equal to n whose largest prime factor is 3. 1
0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

a(n) increases when n has the form 2^a*3^b, with a >= 0 and b > 0.

A distinct sequence can be generated for each prime number; this sequence is for the prime number 3. For an example using another prime number see A301506.

LINKS

Table of n, a(n) for n=0..78.

FORMULA

From David A. Corneth, Mar 27 2018 (Start)

a(n) - a(n - 1) = 1 if and only if n is in 3 * A003586. If n isn't in that sequence then a(n) = a(n - 1).

a(3 * n + b) = A071521(n), n > 0, 0 <= b < 3. (End)

EXAMPLE

a(12) = a(2^2 * 3^1); 3 is the largest prime factor, so a(12) exceeds the previous term by 1. For a(13), 13 is a prime, so there is no increase from the previous term.

MATHEMATICA

Accumulate@ Array[Boole[FactorInteger[#][[-1, 1]] == 3] &, 80, 0] (* Michael De Vlieger, Apr 21 2018 *)

PROG

(MATLAB)

clear; clc;

prime = 3;

limit = 10000;

largest_divisor = ones(1, limit+1);

for k = 0:limit

    f = factor(k);

    largest_divisor(k+1) = f(end);

end

for i = 1:limit+1

    FQN(i) = sum(largest_divisor(1:i)==prime);

end

output = [0:limit; FQN]'

(PARI) gpf(n) = if (n<=1, n, vecmax(factor(n)[, 1]));

a(n) = sum(k=1, n, gpf(k)==3); \\ Michel Marcus, Mar 27 2018

CROSSREFS

Cf. A003586, A065119, A071521.

Cf. A301506.

Sequence in context: A329194 A210533 A246435 * A172471 A046155 A026819

Adjacent sequences:  A301458 A301459 A301460 * A301462 A301463 A301464

KEYWORD

nonn

AUTHOR

Ralph-Joseph Tatt, Mar 21 2018

STATUS

approved

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Last modified July 12 19:26 EDT 2020. Contains 335668 sequences. (Running on oeis4.)