OFFSET
1,1
COMMENTS
All terms except for the last term, 561, are semiprimes (A001358). Semiprimes up to 559 that are not here: 35, 55, 77, 95, 115, 119, 143, 155, 161, 187, 203, 209, 215, 221, 235, 247, 253, 287, 295, 299, 319, 323, 329, 335, 355, 371, 377, 391, 395, 403, 407, 413, 415, 437, 473, 493, 497, 515, 517, 527, 533, 535, 551, 559. - Zak Seidov, Jan 08 2015
The LCM of all terms is 23# * 277# (where # denotes the primorial function A034386), the period of A000790, and therefore also of the related sequence b(n) = gcd(A000790(n), n). - M. F. Hasler, Feb 16 2018
Range of A295997. - Thomas Ordowski, Feb 27 2018
These numbers k < 561 are semiprimes k = pq such that p-1 | q-1, where primes p <= q. Equivalent condition is p-1 | k-1. - Thomas Ordowski, Aug 18 2018
This shows that all even semiprimes < 561 are in this sequence. The odd semiprimes not in this sequence are the semiprimes (equivalently: all terms but 275, 455, 475, 539) less than 561 in A267999 (which equals A121707 up to 695). - M. F. Hasler, Nov 09 2018
LINKS
J. H. Conway, R. K. Guy, W. A. Schneeberger and N. J. A. Sloane, The Primary Pretenders, Acta Arith. 78 (1997), 307-313.
J. H. Conway, R. K. Guy, W. A. Schneeberger and N. J. A. Sloane, The Primary Pretenders, arXiv:math/0207180 [math.NT], 2002.
MATHEMATICA
pp[n_] := For[c = 4, True, c = If[PrimeQ[c+1], c+2, c+1], If[PowerMod[n, c, c] == Mod[n, c], Return[c]]]; seq[n_] := seq[n] = Table[pp[k], {k, 0, 2^n}] // Union; seq[10]; seq[n = 11]; While[ Print["n = ", n, " more terms: ", Complement[seq[n], seq[n-1]]]; seq[n] != seq[n-1], n++]; A108574 = seq[n] (* Jean-François Alcover, Oct 18 2013 *)
PROG
(PARI) my(A=List(561)); forprime(q=2, 561\2, forprime(p=2, min(q, 561\q), (q-1)%(p-1)|| listput(A, p*q))); A108574=Set(A) \\ M. F. Hasler, Nov 09 2018
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
David W. Wilson, Jun 10 2005
STATUS
approved