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

3, 11, 5, 137, 7, 11, 761, 7129, 61, 863, 509, 919, 1117, 41233, 8431, 1138979, 39541, 7440427, 11167027, 18858053, 227, 583859, 467183, 312408463, 34395742267, 215087, 375035183, 4990290163, 17783, 2667653736673, 535919, 199539368321, 15088528003, 137121586897, 9059

Offset: 2

Author

Alexander Adamchuk, Jul 11 2006

Keywords

• nonn

Links

• M. F. Hasler, Table of n, a(n) for n = 2..168

Crossrefs

Cf. A000254, A002547, A001008, A002805, A006530.

Programs

Mathematica

Table[Max[FactorInteger[Sum[1/i,{i,1,n}]/Product[1/i,{i,1,n}]]],{n,2,40}]
FactorInteger[#][[-1,1]]&/@StirlingS1[Range[3,40],2] (* Harvey P. Dale, May 10 2018 *)

PARI

A120299(n)=A006530(A000254(n)) \\ Probably A000254 can be replaced by (much smaller) A096617. - M. F. Hasler, Jul 04 2019

Formula

a(n) = Max[FactorInteger[Sum[1/i,{i,1,n}]/Product[1/i,{i,1,n}]]].

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

Extensions

More terms from M. F. Hasler, Jul 04 2019