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

Author

Alexander Adamchuk, Jul 26 2006

Keywords

• nonn

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

Crossrefs

Cf. A002181, A002445, A051229, A051230.

Programs

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 *)

PARI

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

Formula

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

Extensions

More terms from Alexander Adamchuk, Jul 28 2006