A068191 Numbers n such that A067734(n)=0; complement of A002473; at least one prime-factor of n is larger than 7, it has 2 decimal digits.

11, 13, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 101, 102, 103, 104, 106, 107, 109, 110, 111, 113, 114

Offset: 1

Author

Labos Elemer, Feb 19 2002

Keywords

• base
• nonn

Comments

Also numbers n such that A198487(n) = 0 and A107698(n) = 0. - Jaroslav Krizek, Nov 04 2011

A086299(a(n)) = 0. - Reinhard Zumkeller, Apr 01 2012

A262401(a(n)) < a(n). - Reinhard Zumkeller, Sep 25 2015

Numbers not in A007954. - Mohammed Yaseen, Sep 13 2022

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A002473, A067734.

Cf. A068183, A068184, A068185, A068186, A068187, A068189, A068190.

Cf. A262401.

Programs

Haskell

import Data.List (elemIndices)
a068191 n = a068191_list !! (n-1)
a068191_list = map (+ 1) $ elemIndices 0 a086299_list
-- Reinhard Zumkeller, Apr 01 2012

Mathematica

Select[Range@120, Last@Map[First, FactorInteger@#] > 7 &] (* Vincenzo Librandi, Sep 19 2016 *)

Python

from sympy import integer_log
def A068191(n):
    def f(x):
        c = n
        for i in range(integer_log(x,7)[0]+1):
            i7 = 7**i
            m = x//i7
            for j in range(integer_log(m,5)[0]+1):
                j5 = 5**j
                r = m//j5
                for k in range(integer_log(r,3)[0]+1):
                    c += (r//3**k).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