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

1,1

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

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 *)

Prog

(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
(Haskell)
a102466 n = a102466_list !! (n-1)
a102466_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, A001221, A001222, A000961, A102467, A085156, A086971, A135767.

Sequence in context: A316521 A085156 A342522 * A354144 A322547 A325202

Adjacent sequences: A102463 A102464 A102465 * A102467 A102468 A102469

Keyword

nonn

Author

Reinhard Zumkeller, Jan 09 2005

Status

approved