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%I #8 Aug 09 2017 10:25:38
%S 1,2,17,19,31,38,47,59,61,62,71,94,101,103,107,109,118,122,137,149,
%T 151,157,167,181,197,206,211,218,223,227,229,241,257,263,269,271,283,
%U 289,302,311,313,314,317,331,334,337,347,349,353,361,362,367,379
%N Numbers n such that the Bernoulli number B_{4n} has denominator 30.
%C Most a(n) are primes from A043297(n) except for a(1) = 1 and composite a(n) for n=6,10,12,17,18,26,28,38,39,42,45,50,51, ... a(6) = 38 = 2*19, a(10) = 62 = 2*31, a(12) = 94 = 2*47, a(17) = 118 = 2*59, a(18) = 122 = 2*61, a(26) = 206 = 2*103, a(28) = 218 = 2*109, a(38) = 289 = 17*17, a(39) = 302 = 2*151, a(42) = 314 = 2*157, a(45) = 334 = 2*167, a(50) = 361 = 19*19, a(51) = 362 = 2*181, ... It appears that most composite a(n) are the doubles of some primes from A043297(n) belonging to A081092[n] and A045404[n] - Primes congruent to {3, 4, 5, 6} mod 7. The rest of composite a(n) are the squares of the primes from A043297(n).
%C Some a(n) are the products of different primes from A043297(n), for example a(77) = 527 = 17*31. a(n) belong to A045402 Primes congruent to {1, 3, 4, 5, 6} mod 7. a(n) is a subset of A053176 Primes p such that 2p+1 is composite, A045979 Bernoulli number B_{2n} has denominator 6, A090863 Numbers n such that F(n+1)*F(n-1)*B(2n) is an integer, where F(k)=k-th Fibonacci number and B(2k)=2k-th Bernoulli number. - _Alexander Adamchuk_, Jul 27 2006
%H E. Pérez Herrero, <a href="/A119480/b119480.txt">Table of n, a(n) for n=1..50000</a>
%F a(n) = A051225[n]/2.
%t Select[Range@ 400, Denominator@ BernoulliB[4 #] == 30 &] (* _Michael De Vlieger_, Aug 09 2017 *)
%Y Cf. A043297, A051225, A051222, A051230, A045404.
%Y Cf. A045402, A053176, A045979, A090863.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Jul 26 2006
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