A035113 -id:A035113 - cp's OEIS frontend

A035114 Values of phi(n) corresponding to A035113.

1, 2, 2, 4, 4, 4, 6, 6, 8, 8, 8, 8, 10, 12, 12, 12, 12, 16, 16, 16, 16, 16, 18, 18, 20, 20, 20, 22, 24, 24, 24, 24, 24, 24, 24, 28, 30, 32, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36, 40, 40, 40, 40, 40, 40, 42, 42, 44, 44, 46, 48, 48, 48, 48, 48, 48, 48, 48, 48

Offset: 1

N. J. A. Sloane

			phi(1)=1, phi(3)=2, phi(4)=2, phi(5)=4, ...

Dumitru Damian, Table of n, a(n) for n = 1..10000
L. C. Washington, The Main Conjecture and Annihilation of Class Groups, In: Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, vol 83 (1997) Springer, New York, NY.

Cf. A000010, A035113.

Cf. A002181, A002202, A007614, A014197, A016825, A032447, A058277.

from sympy import totient as A000010
def lov(n): return sorted([[A000010(n), n] for n in range(1,n) if n%4 != 2])
print([x[0] for x in lov(200)][:100]) # Dumitru Damian, Feb 03 2022

a(n) = A000010(A035113(n)). - Michel Marcus, Feb 07 2022

More terms from James Sellers

a(43) onward corrected by Sean A. Irvine, Sep 26 2020

A035115 Relative class number h- of cyclotomic field Q(zeta_m) where m is n-th term of A035113.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 3, 2, 3, 1, 8, 9, 5, 17, 8, 5, 9, 4, 37, 9, 7, 19, 19, 121, 10, 11, 55, 55, 11, 211, 43, 69, 201, 695, 64, 351, 13, 468, 39, 507, 156, 84, 75, 4889, 2593, 1536, 10752, 41241, 76301, 1280, 6795

Offset: 1

N. J. A. Sloane

L. C. Washington, Introduction to Cyclotomic Fields, Springer, p. 353.

Cf. A000010, A035113, A035114, A055513, A061494, A061653.

(* This is only a recomputation of the existing data. *)
terms = 76;
A035113 = Sort[Select[Range[3 terms], Mod[#, 4] != 2&], EulerPhi[#1] <= EulerPhi[#2]&];
A061653 = Import["https://oeis.org/A061653/b061653.txt", "Table"][[All, 2]];
a[n_] := A061653[[A035113[[n]] ]];
Array[a, terms] (* Jean-François Alcover, Aug 17 2019 *)

a(n) = A061653(A035113(n)).

Changed 41421 to 41241, value is given incorrectly in first edition of Washington, Matthew Johnson, Jul 20 2013

A230869 Primes p such that the class number h-tilde_p^{+} of the real cyclotomic field Q(zeta_p + zeta_p^(-1)) is greater than 1.

Original entry on oeis.org

163, 191, 229, 257, 277, 313, 349, 397, 401, 457, 491, 521, 547, 577, 607, 631, 641, 709, 733, 761, 821, 827, 829, 853, 857, 877, 937, 941, 953, 977, 1009, 1063, 1069, 1093, 1129, 1153, 1229, 1231, 1297, 1373, 1381, 1399, 1429, 1459, 1489, 1567, 1601, 1697, 1699, 1777, 1789, 1831, 1861, 1873, 1879, 1889, 1901, 1951

Offset: 1

N. J. A. Sloane, Nov 06 2013

nonn

Taken from the "Main Table" of Schoof.

There is a very slight chance that some primes are missing. In the unlikely event that the number that Schoof calls h-tilde_p is 1, while the actual class number h_p is actually not equal to 1, the prime p would be missing (see the Schoof and Miller articles for details).

John C. Miller, Class numbers of totally real fields and applications to the Weber class number problem, arXiv:1405.1094 [math.NT], 2014.
John C. Miller, Real cyclotomic fields of prime conductor and their class numbers, arXiv:1407.2373 [math.NT], 2014.
Rene Schoof, Class numbers of real cyclotomic fields of prime conductor, Math. Comp., 72 (2002), 913-937.

Cf. A230870 (for the actual class numbers).

See also A000927, A055513, A035113, A035114, A035115.

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A035114 Values of phi(n) corresponding to A035113.

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A035115 Relative class number h- of cyclotomic field Q(zeta_m) where m is n-th term of A035113.

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A230869 Primes p such that the class number h-tilde_p^{+} of the real cyclotomic field Q(zeta_p + zeta_p^(-1)) is greater than 1.

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