A119456 Numbers m such that the Bernoulli number B_{10*m} has denominator 66.

1, 5, 17, 37, 47, 59, 61, 67, 71, 73, 79, 85, 101, 107, 127, 137, 139, 149, 163, 167, 185, 197, 199, 223, 227, 229, 257, 263, 269, 277, 283, 289, 295, 305, 307, 311, 313, 317, 331, 335, 347, 353, 355, 365, 373, 379, 383, 389, 395, 397, 401, 433, 449, 457, 461

Offset

1,2

Comments

Subset of A002181 (inverse of the Euler totient function).

Most terms are primes except for n = 12, 21, 32, 33, 34, 40, ... because a(12) = 85 = 5*17, a(21) = 185 = 5*37, a(32) = 289 = 17*17, a(33) = 295 = 5*59, a(34) = 305 = 5*61, a(40) = 335 = 5*67, ... Each composite term appears to be a product of two primes from previous terms or a square of a prime from previous terms.

Composite terms are the products of powers of primes that are factors of previous terms. For example, there are terms equal to 17, 17^2, 5*17^2, 59^2, 59*61, 61^2, 61*67, 67^2, 67*73, 17^3, 5*17*59, 71*73, 5*17*61, 73^2, 71*79, 73*79, 5*17*73, 79^2, 61*167, 101^2, 37*277, 5*37*59, 79*139, 107^2, 5*17*139, 5*37*67, 5*37*71, 17^2*47, 61*223, 61*227, 5*17*163, 5*17*167, 71*227, 127^2, 17^2*59, 5*59^2, 17^2*61, 5*61^2, 137^2, 137*139, 139^2, 17^2*67, 5*17*229, 137*149, 5*61*67, 5*59*71, 17^2*73, 5*67^2, 5*61*79, 5*67*73, 5*17^3, ... - Alexander Adamchuk, Jul 28 2006

Links

E. Pérez Herrero, Table of n, a(n) for n=1..50000

Formula

a(n) = A051230(n)/10 = A051229(n)/5.

Mathematica

Do[s=1+Divisors[n]; s1=Flatten[Position[PrimeQ[s], True]]; s2=Part[s, s1]; If[Equal[s2, {2, 3, 11}], Print[n/10]], {n, 1, 50000}] (* Alexander Adamchuk, Jul 28 2006 *)

Prog

(PARI) isok(m) = denominator(bernfrac(10*m)) == 66; \\ Michel Marcus, May 31 2022

Crossrefs

Cf. A002181, A002445, A051229, A051230.

Sequence in context: A321658 A080167 A060245 * A264904 A257582 A339988

Adjacent sequences: A119453 A119454 A119455 * A119457 A119458 A119459

Keyword

nonn

Author

Alexander Adamchuk, Jul 26 2006

Extensions

More terms from Alexander Adamchuk, Jul 28 2006

Status

approved