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A081062
Neither 3-smooth numbers nor prime powers.
6
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
1,1
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
LINKS
EXAMPLE
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
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 *)
PROG
(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
CROSSREFS
Sequence in context: A246449 A121836 A317590 * A330136 A307589 A209800
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Mar 04 2003
STATUS
approved