A064911 If n is semiprime (or 2-almost prime) then 1 else 0.

0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Patrick De Geest, Oct 13 2001

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65545 (first 10000 terms from Reinhard Zumkeller)
• Eric Weisstein's World of Mathematics, Semiprime
• Eric Weisstein's World of Mathematics, Prime zeta function primezeta(s).
• Index entries for characteristic functions
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A010051, A064899-A064910, A053409, A046413, A101040, A105700, A280710, A302047, A302048, A302049, A353475, A353476, A353477, A353478, A353479, A353480, A353481.

Programs

Haskell

a064911 = a010051 . a032742 -- Reinhard Zumkeller, Mar 13 2011

Maple

with(numtheory):
a:= n-> `if`(bigomega(n)=2, 1, 0):
seq(a(n), n=1..120);  # Alois P. Heinz, Mar 16 2011

Mathematica

Table[If[PrimeOmega[n] == 2, 1, 0], {n, 105}] (* Jayanta Basu, May 25 2013 *)

PARI

a(n)=bigomega(n)==2 \\ Charles R Greathouse IV, Mar 13 2011

Formula

a(n) = 1 iff n is in A001358 (semiprimes), a(n) = 0 iff n is in A100959 (non-semiprimes). - Reinhard Zumkeller, Nov 24 2004

Dirichlet g.f.: (primezeta(2s) + primezeta(s)^2)/2. - Franklin T. Adams-Watters, Jun 09 2006

a(n) = A057427(A174956(n)); a(n)*A072000(n) = A174956(n). - Reinhard Zumkeller, Apr 03 2010

a(n) = A010051(A032742(n)) (i.e., largest proper divisor is prime). - Reinhard Zumkeller, Mar 13 2011

From Antti Karttunen, Apr 24 2018 & Apr 22 2022: (Start)

a(n) = A280710(n) + A302048(n) = A101040(n) - A010051(n).

a(n) = A353478(n) + A353480(n) = A353477(n) + A353478(n) + A353479(n).

a(n) = A353475(n) + A353476(n).

(End)

a(n) = [Omega(n) = 2], where [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jul 22 2025

Extensions

Edited by M. F. Hasler, Oct 18 2017