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A119480
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Numbers n such that the Bernoulli number B_{4n} has denominator 30.
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28
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1, 2, 17, 19, 31, 38, 47, 59, 61, 62, 71, 94, 101, 103, 107, 109, 118, 122, 137, 149, 151, 157, 167, 181, 197, 206, 211, 218, 223, 227, 229, 241, 257, 263, 269, 271, 283, 289, 302, 311, 313, 314, 317, 331, 334, 337, 347, 349, 353, 361, 362, 367, 379
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OFFSET
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1,2
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COMMENTS
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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).
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
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range@ 400, Denominator@ BernoulliB[4 #] == 30 &] (* Michael De Vlieger, Aug 09 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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