OFFSET
1,2
COMMENTS
Conjecture: (i) a(n) is prime for any n > 3.
(ii) For the n-th Springer number S_n given by A001586, if n is greater than one and not equal to 5, then S_n has a prime divisor which does not divide any S_k with k < n.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..54
EXAMPLE
a(4) = 17 since T_4 = 2^4*17 with 17 dividing none of T_1 = 1, T_2 = 2 and T_3 = 2^4.
MATHEMATICA
t[n_]:=(-1)^(n-1)*2^(2n)(2^(2n)-1)BernoulliB[2n]/(2n)
f[n_]:=FactorInteger[t[n]]
p[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[t[n]<2, Goto[cc]]; Do[Do[If[Mod[t[i], Part[p[n], k]]==0, Goto[aa]], {i, 1, n-1}]; Print[n, " ", Part[p[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[p[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 40}]
PROG
(Sage) # uses[LPDtransform from A242193]
def Tnum(n): return (-1)^(n-1)*2^(2*n)*(2^(2*n)-1)*bernoulli(2*n)/(2*n)
A242195list = lambda sup: [LPDtransform(n, Tnum) for n in (1..sup)]
print(A242195list(40)) # Peter Luschny, Jul 26 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 07 2014
STATUS
approved