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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 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.)