The On-Line Encyclopedia of Integer Sequences (OEIS)

A214044 revision #11

A214044

Odd squarefree semiprimes n for which (n - d1)/(d1^2 - d1) = (d2^2 - d2)/(n - d2) = k, where d1 and d2 are the two prime factors of n and k is a natural number.

15, 21, 33, 39, 51, 57, 65, 69, 85, 87, 91, 93, 111, 123, 129, 133, 141, 145, 159, 177, 183, 185, 201, 205, 213, 217, 219, 237, 249, 259, 265, 267, 291, 301, 303, 305, 309, 321, 327, 339, 341, 365, 381, 393, 411, 417, 427, 445, 447, 451, 453, 469, 471, 481, 485, 489, 501, 505, 511, 515, 535, 545, 553, 565, 635

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OFFSET

1,1

COMMENTS

All these numbers n are Fermat pseudoprimes (as odd squarefree semiprimes) for at least two bases 1 < b < n - 1.

It is interesting that all the numbers from the sequence above are Fermat pseudoprimes to base d2, d2 - 1 and d2 + 1.

LINKS

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Fermat Pseudoprime

CROSSREFS

Cf. A046388, A175101, A181780.

Sequence in context: A300117 * A177516 A127329 A043326 A179996 A079814

Adjacent sequences: A214041 A214042 A214043 * A214045 A214046 A214047

KEYWORD

nonn,changed

AUTHOR

Marius Coman, Jul 02 2012

STATUS

editing