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A119315
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Numbers with composite numbers as third divisors.
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6
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4, 8, 9, 16, 20, 25, 27, 28, 32, 40, 44, 49, 52, 56, 64, 68, 76, 80, 81, 88, 92, 99, 100, 104, 112, 116, 117, 121, 124, 125, 128, 136, 140, 148, 152, 153, 160, 164, 169, 171, 172, 176, 184, 188, 196, 200, 207, 208, 212, 220, 224, 232, 236, 243, 244, 248, 256, 260
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OFFSET
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1,1
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COMMENTS
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m is a term iff A067029(m) > 1 and (A001221(m) = 1 or A020639(m)^2 <= A119288(m)).
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 3, 23, 221, 2194, 21895, 219307, 2193435, 21937419, 219396872, 2193979781, ... . Apparently, the asymptotic density of this sequence exists and equals 0.219... . - Amiram Eldar, Jul 02 2022
Numbers k such that A292269(k) is composite, which must then be a square of prime (A001248) by necessity. - Antti Karttunen, Jul 02 2022
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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Select[Range[300], CompositeQ[Divisors[#][[3]]]&]//Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 03 2021 *)
Select[Range[260], (f = FactorInteger[#])[[1, 2]] > 1 && (Length[f] == 1 || f[[1, 1]]^2 < f[[2, 1]]) &] (* Amiram Eldar, Jul 02 2022 *)
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PROG
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(PARI)
A355453(n) = ((n>1) && !isprime(n) && !isprime(divisors(n)[3]));
isA119315(n) = A355453(n); \\ Antti Karttunen, Jul 02 2022
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CROSSREFS
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Complement of A119316.
A025475, A092259, and A355445 are subsequences.
Cf. A000005, A001221, A001248, A002808, A020639, A027750, A067029, A292269, A355453 (characteristic function).
Cf. also A355455.
Sequence in context: A162215 A134344 A324278 * A346256 A010390 A003624
Adjacent sequences: A119312 A119313 A119314 * A119316 A119317 A119318
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, May 15 2006
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STATUS
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approved
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