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A120299 Largest prime factor of Stirling numbers of first kind s(n,2) = A000254(n). 2


%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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Last modified April 12 21:13 EDT 2021. Contains 342932 sequences. (Running on oeis4.)