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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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90
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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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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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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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PROG
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(Haskell)
a046388 n = a046388_list !! (n-1)
a046388_list = filter ((== 2) . a001221) a056911_list
(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
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CROSSREFS
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Cf. A353481 (characteristic function).
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KEYWORD
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nonn
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AUTHOR
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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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