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A308971 Largest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.

%I A308971 #18 Feb 24 2020 08:07:51
%S A308971 1,3,11,5,137,7,11,761,7129,61,863,509,919,1117,41233,8431,1138979,
%T A308971 39541,7440427,11167027,18858053,227,583859,467183,312408463,
%U A308971 34395742267,215087,375035183,4990290163,17783,2667653736673,535919,199539368321,15088528003,137121586897
%N A308971 Largest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.
%C A308971 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 A308971 Amiram Eldar, <a href="/A308971/b308971.txt">Table of n, a(n) for n = 1..325</a>
%F A308971 a(n) = A006530(A001008(n)). - _Amiram Eldar_, Feb 24 2020
%e A308971    n | A001008(n) written as product of primes
%e A308971 -----+------------------------------------------
%e A308971    1 | 1 (empty product)
%e A308971    2 | 3
%e A308971    3 | 11
%e A308971    4 | 5 * 5
%e A308971    5 | 137
%e A308971    6 | 7 * 7
%e A308971    7 | 3 * 11 * 11
%e A308971    8 | 761
%e A308971    9 | 7129
%e A308971   10 | 11 * 11 * 61
%e A308971   11 | 97 * 863
%e A308971   12 | 13 * 13 * 509
%e A308971   13 | 29 * 43 * 919
%e A308971   14 | 1049 * 1117
%e A308971   15 | 29 * 41233
%e A308971   16 | 17 * 17 * 8431
%e A308971   17 | 37 * 1138979
%e A308971   18 | 19 * 19 * 39541
%e A308971   19 | 37 * 7440427
%e A308971   20 | 5 * 11167027
%e A308971 etc., therefore this sequence = 1, 3, 11, 5, 137, 7, 11, 761, 7129, 61, ...
%t A308971 Array[FactorInteger[Numerator@HarmonicNumber[#]][[-1, 1]] &, 35] (* _Michael De Vlieger_, Jul 04 2019 *)
%o A308971 (PARI) a(n)={if(n>1, factor(A001008(n))[1,1], 1)}
%Y A308971 Cf. A001008, A006530.
%Y A308971 Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308970 (smallest prime factor) of A001008(n).
%K A308971 nonn
%O A308971 1,2
%A A308971 _M. F. Hasler_, Jul 03 2019