A102466 Numbers such that the number of divisors is the sum of numbers of prime factors with and without repetitions.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 67, 69, 71, 73, 74, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109

Offset: 1

Author

Reinhard Zumkeller, Jan 09 2005

Keywords

• nonn

Comments

A000005(a(n)) = A001221(a(n)) + A001222(a(n)); prime powers are a subsequence (A000961); complement of A102467; not the same as A085156.

Equals { n | omega(n)=1 or Omega(n)=2 }, that is, these are exactly the prime powers (>1) and semiprimes. - M. F. Hasler, Jan 14 2008

For n > 1: A086971(a(n)) <= 1. - Reinhard Zumkeller, Dec 14 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A001221, A001222, A000961, A102467, A085156, A086971, A135767.

Programs

Haskell

a102466 n = a102466_list !! (n-1)
a102466_list = [x | x <- [1..], a000005 x == a001221 x + a001222 x]
-- Reinhard Zumkeller, Dec 14 2012

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[110],DivisorSigma[0,#]==PrimeOmega[#]+PrimeNu[#]&] (* Harvey P. Dale, Mar 09 2016 *)

PARI

is(n)=my(f=factor(n)[,2]); #f==1 || f==[1,1]~ \\ Charles R Greathouse IV, Oct 19 2015

Sage

def is_A102466(n) :
    return bool(sloane.A001221(n) == 1 or sloane.A001222(n) == 2)
def A102466_list(n) :
    return [k for k in (1..n) if is_A102466(k)]
A102466_list(109)  # Peter Luschny, Feb 08 2012