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a(n) = A190339(n)/A224911(n).
2

%I #17 Mar 17 2018 05:40:52

%S 1,2,3,15,15,21,1155,165,2145,51051,255255,440895,440895,969,111435,

%T 248834355,248834355,2927463,5898837945,44352165,1641030105,

%U 8563193457,42815967285,80047243185,1360803134145,32898537309,7731156267615,1028243783592795,1028243783592795,375840831244263

%N a(n) = A190339(n)/A224911(n).

%C Are non-repeated terms of A224911(n) (2,3,5,11,17,...) A124588(n+1)?

%C Are repeated terms of A224911(n) (7,13,19,23,31,37,...) A049591(n+1)? At that sequence, _Benoit Cloitre_ mentions a link to the Bernoulli numbers.

%C Greatest primes dividing a(n): 1, 2, 3, 5, 5, 7, 11, 11, 13, 17, 17, 19, 19, 19, 23, 29, 29, 29, ... = b(n). It appears that b(n) is A224911(n) with A008578(n), ancient primes, instead of A000040(n).

%C Hence c(n) = 2, 6, 15, 35, ... = 2, followed by A006094(n+1).

%H Vincenzo Librandi, <a href="/A238691/b238691.txt">Table of n, a(n) for n = 0..200</a>

%e a(0)=2/2=1, a(1)=6/3=2, a(2)=15/5=3, a(3)=a(4)=105/7=15, ... .

%t nmax = 40; b[n_] := BernoulliB[n]; b[1] = 1/2; bb = Table[b[n], {n, 0, 2*nmax-1}]; diff = Table[Differences[bb, n], {n, 1, nmax}]; (#/FactorInteger[#][[-1, 1]])& /@ Denominator[Diagonal[diff]]

%Y Cf. A060308.

%K nonn

%O 0,2

%A _Paul Curtz_, Mar 03 2014

%E a(16)-a(25) from _Jean-François Alcover_, Mar 03 2014