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%I #12 Jul 04 2019 03:43:09
%S 3,11,5,137,7,11,761,7129,61,863,509,919,1117,41233,8431,1138979,
%T 39541,7440427,11167027,18858053,227,583859,467183,312408463,
%U 34395742267,215087,375035183,4990290163,17783,2667653736673,535919,199539368321,15088528003,137121586897,9059
%N Largest prime factor of Stirling numbers of first kind s(n,2) = A000254(n).
%H M. F. Hasler, <a href="/A120299/b120299.txt">Table of n, a(n) for n = 2..168</a>
%F a(n) = Max[FactorInteger[Sum[1/i,{i,1,n}]/Product[1/i,{i,1,n}]]].
%F a(n) = gpf(A096617(n)), where gpf = A006530 is the greatest prime factor, and A096617 is a "reduced" variant of A001008 and thus A000254. [Conjectured; true if this gpf is always > n.] - _M. F. Hasler_, Jul 04 2019
%t Table[Max[FactorInteger[Sum[1/i,{i,1,n}]/Product[1/i,{i,1,n}]]],{n,2,40}]
%t FactorInteger[#][[-1,1]]&/@StirlingS1[Range[3,40],2] (* _Harvey P. Dale_, May 10 2018 *)
%o (PARI) A120299(n)=A006530(A000254(n)) \\ Probably A000254 can be replaced by (much smaller) A096617. - _M. F. Hasler_, Jul 04 2019
%Y Cf. A000254, A002547, A001008, A002805, A006530.
%K nonn
%O 2,1
%A _Alexander Adamchuk_, Jul 11 2006
%E More terms from _M. F. Hasler_, Jul 04 2019
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