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A308970 Smallest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.

%I A308970 #13 Jul 02 2025 13:54:44
%S A308970 1,3,11,5,137,7,3,761,7129,11,97,13,29,1049,29,17,37,19,37,5,18858053,
%T A308970 3,761,5,109,34395742267,521,29,43,31,109,2917,269,3583,397,37,
%U A308970 10839223,199,737281,41,85691034670497533,7,140473,109,1553,47,911,7,23982193,61,227,53,941,5953
%N A308970 Smallest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.
%C A308970 Row 1 is taken to be {1} instead of being empty, by convention.
%C A308970 This is the first column of A308968 and A308969, which list the prime factors of A001008.
%H A308970 Chai Wah Wu, <a href="/A308970/b308970.txt">Table of n, a(n) for n = 1..325</a>
%e A308970    n | A001008(n) written as product of primes
%e A308970 -----+------------------------------------------
%e A308970    1 | 1 (empty product)
%e A308970    2 | 3
%e A308970    3 | 11
%e A308970    4 | 5 * 5
%e A308970    5 | 137
%e A308970    6 | 7 * 7
%e A308970    7 | 3 * 11 * 11
%e A308970    8 | 761
%e A308970    9 | 7129
%e A308970   10 | 11 * 11 * 61
%e A308970   11 | 97 * 863
%e A308970   12 | 13 * 13 * 509
%e A308970   13 | 29 * 43 * 919
%e A308970   14 | 1049 * 1117
%e A308970   15 | 29 * 41233
%e A308970   16 | 17 * 17 * 8431
%e A308970   17 | 37 * 1138979
%e A308970   18 | 19 * 19 * 39541
%e A308970   19 | 37 * 7440427
%e A308970   20 | 5 * 11167027
%e A308970 etc., therefore this sequence = 1, 3, 11, 5, 137, 7, 3, 761, ...
%t A308970 FactorInteger[#][[1,1]]&/@Numerator[HarmonicNumber[Range[60]]] (* _Harvey P. Dale_, Jul 02 2025 *)
%o A308970 (PARI) row(n)={if(n>1, factor(A001008(n))[1,1], 1)}
%Y A308970 Cf. A001008.
%Y A308970 Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308971 (greatest prime factor) of A001008(n).
%K A308970 nonn
%O A308970 1,2
%A A308970 _M. F. Hasler_, Jul 03 2019