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A064911
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If n is semiprime (or 2-almost prime) then 1 else 0.
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74
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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
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listen;
history;
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OFFSET
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1,1
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LINKS
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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
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FORMULA
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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)
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MAPLE
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with(numtheory):
a:= n-> `if`(bigomega(n)=2, 1, 0):
seq(a(n), n=1..120); # Alois P. Heinz, Mar 16 2011
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MATHEMATICA
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Table[If[PrimeOmega[n] == 2, 1, 0], {n, 105}] (* Jayanta Basu, May 25 2013 *)
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PROG
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(Haskell) a064911 = a010051 . a032742 -- Reinhard Zumkeller, Mar 13 2011
(PARI) a(n)=bigomega(n)==2 \\ Charles R Greathouse IV, Mar 13 2011
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CROSSREFS
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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 A360125
Adjacent sequences: A064908 A064909 A064910 * A064912 A064913 A064914
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest, Oct 13 2001
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EXTENSIONS
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Edited by M. F. Hasler, Oct 18 2017
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STATUS
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approved
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