

A102467


Positive integers k, such that d(k) <> Omega(k) + omega(k), where d = A000005, Omega = A001222 and omega = A001221.


8



1, 12, 18, 20, 24, 28, 30, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 126, 130, 132, 135, 136, 138, 140, 144, 147, 148, 150, 152, 153, 154, 156
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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


FORMULA

Complement of A102466; A000005(a(n)) <> A001221(a(n)) + A001222(a(n)).
For n > 1, A086971(a(n)) > 1.  Reinhard Zumkeller, Dec 14 2012
Characteristic function: 1  [d(n) = Omega(n) + omega(n)], where [] is the Iverson bracket.  Wesley Ivan Hurt, Apr 25 2020


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


MATHEMATICA

Select[Range[200], DivisorSigma[0, #] != PrimeOmega[#] + PrimeNu[#]&] (* JeanFrançois Alcover, Jun 22 2018 *)


PROG

(Sage)
def is_A102467(n) :
return sloane.A001221(n) != 1 and sloane.A001222(n) != 2
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 !! (n1)
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

Cf. A000005 (tau), A001221 (omega), A001222 (Omega).
Cf. A102466, A135767.
Sequence in context: A271345 A007624 A036456 * A126706 A123711 A200511
Adjacent sequences: A102464 A102465 A102466 * A102468 A102469 A102470


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jan 09 2005


EXTENSIONS

Name changed by Wesley Ivan Hurt, Apr 25 2020


STATUS

approved



