A081062 Neither 3-smooth numbers nor prime powers.

10, 14, 15, 20, 21, 22, 26, 28, 30, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 50, 51, 52, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100, 102, 104, 105, 106, 110, 111, 112, 114, 115, 116

Offset: 1

Author

Reinhard Zumkeller, Mar 04 2003

Keywords

• nonn
• easy

Comments

A081060(m) > 1 iff m = a(k) for some k. - corrected by Gionata Neri, Jul 30 2016

Complement of A081061.

Composites with smallest prime factor^largest prime factor > largest prime factor^smallest prime factor. - Juri-Stepan Gerasimov, Jan 04 2009

Examples

			12 = 2^2*3 is not in the sequence because it is 3-smooth (all prime factors are 3 or less). 17 = 17^1 and 49 = 7^2 are not in the sequence because they are prime powers. - _Michael B. Porter_, Jul 31 2016
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A000961.

Programs

Maple

filter:= proc(n) local f; f:= numtheory:-factorset(n); nops(f) > 1 and max(f) > 3 end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 31 2016

Mathematica

Select[Range@ 120, Nor[PrimePowerQ@ #, 3 EulerPhi[6 #] == 6 #] &] (* Michael De Vlieger, Aug 02 2016, after Robert G. Wilson v at A003586 *)

Python

from sympy import integer_log, primepi, integer_nthroot
def A081062(n):
    def f(x): return int(n+1-(a:=x.bit_length())-(b:=integer_log(x,3)[0])+sum((x//3**i).bit_length() for i in range(b+1))+sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, a)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 16 2024