A308971 - OEIS

%I #18 Feb 24 2020 08:07:51

%S 1,3,11,5,137,7,11,761,7129,61,863,509,919,1117,41233,8431,1138979,

%T 39541,7440427,11167027,18858053,227,583859,467183,312408463,

%U 34395742267,215087,375035183,4990290163,17783,2667653736673,535919,199539368321,15088528003,137121586897

%N Largest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.

%C Initial terms coincide with A120299 = greatest prime factor of Stirling numbers of first kind A000254. They differ when the unreduced denominator of H(n), equal to n!, is divisible by this factor, i.e., A120299(n) <= n. Can this ever happen?

%H Amiram Eldar, <a href="/A308971/b308971.txt">Table of n, a(n) for n = 1..325</a>

%F a(n) = A006530(A001008(n)). - _Amiram Eldar_, Feb 24 2020

%e    n | A001008(n) written as product of primes

%e -----+------------------------------------------

%e    1 | 1 (empty product)

%e    2 | 3

%e    3 | 11

%e    4 | 5 * 5

%e    5 | 137

%e    6 | 7 * 7

%e    7 | 3 * 11 * 11

%e    8 | 761

%e    9 | 7129

%e   10 | 11 * 11 * 61

%e   11 | 97 * 863

%e   12 | 13 * 13 * 509

%e   13 | 29 * 43 * 919

%e   14 | 1049 * 1117

%e   15 | 29 * 41233

%e   16 | 17 * 17 * 8431

%e   17 | 37 * 1138979

%e   18 | 19 * 19 * 39541

%e   19 | 37 * 7440427

%e   20 | 5 * 11167027

%e etc., therefore this sequence = 1, 3, 11, 5, 137, 7, 11, 761, 7129, 61, ...

%t Array[FactorInteger[Numerator@HarmonicNumber[#]][[-1, 1]] &, 35] (* _Michael De Vlieger_, Jul 04 2019 *)

%o (PARI) a(n)={if(n>1, factor(A001008(n))[1,1], 1)}

%Y Cf. A001008, A006530.

%Y Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308970 (smallest prime factor) of A001008(n).

%K nonn

%O 1,2

%A _M. F. Hasler_, Jul 03 2019