A279622 Numbers with a prime factor greater than 5.

7, 11, 13, 14, 17, 19, 21, 22, 23, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..9825

Formula

a(n) = n + O(log^3 n). - Charles R Greathouse IV, Dec 22 2016

Mathematica

fQ[n_]:=!PowerMod[30, n, n] == 0; Select[Range[100], fQ]
Select[Range[100], Max[FactorInteger[#][[;; , 1]]]>5&] (* Harvey P. Dale, Feb 28 2023 *)

Prog

(PARI) isok(n) = vecmax(factor(n)[, 1]) > 5; \\ Michel Marcus, Dec 21 2016
(PARI) is(n)=if(n<7, return(0)); n>>=valuation(n, 2); n/=3^valuation(n, 2) * 5^valuation(n, 5); n>1 \\ Charles R Greathouse IV, Dec 22 2016
(Magma) [n: n in [1..100] | not PrimeDivisors(n) subset [2, 3, 5]]; // Vincenzo Librandi, Jan 29 2017
(Python)
from sympy import integer_log
def A279622(n):
    def f(x):
        c = n
        for i in range(integer_log(x, 5)[0]+1):
            for j in range(integer_log(y:=x//5**i, 3)[0]+1):
                c += (y//3**j).bit_length()
        return c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 16 2024

Crossrefs

Complement of A051037.

Cf. A059485.

Sequence in context: A091901 A072823 A110547 * A247819 A051660 A364562

Adjacent sequences: A279619 A279620 A279621 * A279623 A279624 A279625

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 21 2016

Status

approved