OFFSET
1,2
COMMENTS
These are the numbers which are neither prime powers (>1) nor semiprimes. - M. F. Hasler, Jan 31 2008
For n > 1, positive integers k with a composite divisor, d < k, that is relatively prime to k/d. For example 12 is in the sequence since 4 (composite) is coprime to 12/4 = 3. - Wesley Ivan Hurt, Apr 25 2020
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Joerg Arndt, Matters Computational (The Fxtbook), section 40.4.1.3 "Testing for irreducibility without GCD computations", pp. 839-840.
FORMULA
EXAMPLE
10 is not in the sequence since d(10) = 4 is equal to Omega(10) + omega(10) = 2 + 2 = 4.
12 is in the sequence since d(12) = 6 is not equal to Omega(12) + omega(12) = 3 + 2 = 5. - Wesley Ivan Hurt, Apr 25 2020
MAPLE
with(numtheory):
q:= n-> is(tau(n)<>bigomega(n)+nops(factorset(n))):
select(q, [$1..200])[]; # Alois P. Heinz, Jul 14 2023
MATHEMATICA
Select[Range[200], DivisorSigma[0, #] != PrimeOmega[#] + PrimeNu[#]&] (* Jean-François Alcover, Jun 22 2018 *)
PROG
(Sage)
def is_A102467(n) :
def A102467_list(n) :
return [k for k in (1..n) if is_A102467(k)]
A102467_list(156) # Peter Luschny, Feb 07 2012
(Haskell)
a102467 n = a102467_list !! (n-1)
a102467_list = [x | x <- [1..], a000005 x /= a001221 x + a001222 x]
-- Reinhard Zumkeller, Dec 14 2012
(PARI) is(n)=my(f=factor(n)[, 2]); #f!=1 && f!=[1, 1]~ \\ Charles R Greathouse IV, Oct 19 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 09 2005
EXTENSIONS
Name changed by Wesley Ivan Hurt, Apr 25 2020
STATUS
approved