A119456 - OEIS

%I #25 Aug 17 2024 09:50:20

%S 1,5,17,37,47,59,61,67,71,73,79,85,101,107,127,137,139,149,163,167,

%T 185,197,199,223,227,229,257,263,269,277,283,289,295,305,307,311,313,

%U 317,331,335,347,353,355,365,373,379,383,389,395,397,401,433,449,457,461

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

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

%C 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.

%C 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

%H E. Pérez Herrero, <a href="/A119456/b119456.txt">Table of n, a(n) for n=1..50000</a>

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

%t 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 *)

%o (PARI) isok(m) = denominator(bernfrac(10*m)) == 66; \\ _Michel Marcus_, May 31 2022

%Y Cf. A002181, A002445, A051229, A051230.

%K nonn

%O 1,2

%A _Alexander Adamchuk_, Jul 26 2006

%E More terms from _Alexander Adamchuk_, Jul 28 2006