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A046388
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Odd numbers of the form p*q where p and q are distinct primes.
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86
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15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111, 115, 119, 123, 129, 133, 141, 143, 145, 155, 159, 161, 177, 183, 185, 187, 201, 203, 205, 209, 213, 215, 217, 219, 221, 235, 237, 247, 249, 253, 259, 265, 267, 287, 291, 295, 299, 301, 303
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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These are the odd squarefree semiprimes.
These numbers k have the property that k is a Fermat pseudoprime for at least two bases 1 < b < k - 1. That is, b^(k - 1) == 1 (mod k). See sequence A175101 for the number of bases. - Karsten Meyer, Dec 02 2010
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
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FORMULA
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Sum_{n>=1} 1/a(n)^s = (1/2)*(P(s)^2 - P(2*s)) + 1/4^s - P(s)/2^s, for s>1, where P is the prime zeta function. - Amiram Eldar, Nov 21 2020
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MATHEMATICA
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max = 300; A046388 = Sort@Flatten@Table[Prime[m] Prime[n], {n, 3, Ceiling[PrimePi[max/3]]}, {m, 2, n - 1}]; Select[A046388, # < max &] (* Alonso del Arte based on Robert G. Wilson v's program for A006881, Oct 24 2011 *)
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PROG
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(Haskell)
a046388 n = a046388_list !! (n-1)
a046388_list = filter ((== 2) . a001221) a056911_list
-- Reinhard Zumkeller, Jan 02 2014
(PARI) isok(n) = (n % 2) && (bigomega(n) == 2) && (omega(n)==2); \\ Michel Marcus, Feb 05 2015
(Python)
from sympy import factorint
def ok(n):
if n < 2 or n%2 == 0: return False
f = factorint(n)
return len(f) == 2 and sum(f.values()) == 2
print([k for k in range(304) if ok(k)]) # Michael S. Branicky, May 03 2022
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CROSSREFS
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Intersection of A005117 and A046315, or equally, of A005408 and A006881, or of A001358 and A056911.
Union of A080774 and A190299, which the latter is the union of A131574 and A016105.
Subsequence of A024556 and of A225375.
Cf. A353481 (characteristic function).
Cf. A001221, A046404, A056911, A175101.
Different from A056913, A098905, A225375.
Sequence in context: A329229 A146166 A024556 * A056913 A002557 A128907
Adjacent sequences: A046385 A046386 A046387 * A046389 A046390 A046391
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest, Jun 15 1998
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EXTENSIONS
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I removed some ambiguity in the definition and edited the entry, merging in some material from A146166. - N. J. A. Sloane, May 09 2013
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STATUS
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approved
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