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 A344079 Numbers m such that A060649(m) > 0 and that C(-A060649(m)) is not cyclic, where C(D) is the class group of the quadratic field with discriminant D. 0
 12, 16, 20, 72, 88, 92, 104, 128, 136, 164, 172, 184, 188, 192, 236, 243, 244, 256, 260, 264, 272, 276, 284, 292, 296, 316, 332, 336, 340, 342, 344, 348, 364, 372, 376, 388, 392, 396, 400, 416, 420, 440, 456, 468, 484, 488, 496, 504, 536, 548, 560, 576, 596, 600, 608, 612, 620, 637, 640, 644, 652, 664 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Assume that for all n, we have A060649(n) > 0 and either A344072(n) = 0 or A344072(n) > A060649(2n), then this sequence gives the indices where A060649 and A344073 differ. All terms must be nonsquarefree, since an abelian group of squarefree order must be cyclic. LINKS EXAMPLE The smallest k == 3 (mod 4) such that Q(sqrt(-k)) has class number 12 is k = -231, but the class group of Q(sqrt(-231)) is isomorphic to C_2 X C_6, which is not cyclic, so 12 is a term. The smallest k == 3 (mod 4) such that Q(sqrt(-k)) has class number 20 is k = -455, but the class group of Q(sqrt(-455)) is isomorphic to C_2 X C_10, which is not cyclic, so 20 is a term. The smallest k == 3 (mod 4) such that Q(sqrt(-k)) has class number 637 is k = -149519, but the class group of Q(sqrt(-149519)) is isomorphic to C_7 X C_91, which is not cyclic, so 637 is a term. PROG (PARI) isA344079(n) = my(d=3); while(!isfundamental(-d) || qfbclassno(-d)!=n, d+=4); #quadclassunit(-d)>1 CROSSREFS Cf. A060649, A344073, A344072. Sequence in context: A337700 A243538 A183052 * A240052 A070329 A064695 Adjacent sequences:  A344076 A344077 A344078 * A344080 A344081 A344082 KEYWORD nonn AUTHOR Jianing Song, May 08 2021 STATUS approved

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Last modified January 28 12:35 EST 2022. Contains 350656 sequences. (Running on oeis4.)