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

1,1

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

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)

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 *)

Prog

(Haskell) a064911 = a010051 . a032742 -- Reinhard Zumkeller, Mar 13 2011
(PARI) a(n)=bigomega(n)==2 \\ Charles R Greathouse IV, Mar 13 2011

Crossrefs

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

Sequence in context: A353476 A288377 A341609 * A174898 A099618 A361496

Adjacent sequences: A064908 A064909 A064910 * A064912 A064913 A064914

Keyword

nonn

Author

Patrick De Geest, Oct 13 2001

Extensions

Edited by M. F. Hasler, Oct 18 2017

Status

approved