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

Author

Vincenzo Librandi, Dec 21 2016

Keywords

• nonn
• easy

Links

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

Crossrefs

Complement of A051037.

Cf. A059485.

Programs

Magma

[n: n in [1..100] | not PrimeDivisors(n) subset [2, 3, 5]]; // Vincenzo Librandi, Jan 29 2017

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 *)

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

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

Formula

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