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A308971
Largest prime factor of A001008(n), numerator of n-th harmonic number; a(1) = 1.
5
1, 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
OFFSET
1,2
COMMENTS
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?
LINKS
FORMULA
a(n) = A006530(A001008(n)). - Amiram Eldar, Feb 24 2020
EXAMPLE
n | A001008(n) written as product of primes
-----+------------------------------------------
1 | 1 (empty product)
2 | 3
3 | 11
4 | 5 * 5
5 | 137
6 | 7 * 7
7 | 3 * 11 * 11
8 | 761
9 | 7129
10 | 11 * 11 * 61
11 | 97 * 863
12 | 13 * 13 * 509
13 | 29 * 43 * 919
14 | 1049 * 1117
15 | 29 * 41233
16 | 17 * 17 * 8431
17 | 37 * 1138979
18 | 19 * 19 * 39541
19 | 37 * 7440427
20 | 5 * 11167027
etc., therefore this sequence = 1, 3, 11, 5, 137, 7, 11, 761, 7129, 61, ...
MATHEMATICA
Array[FactorInteger[Numerator@HarmonicNumber[#]][[-1, 1]] &, 35] (* Michael De Vlieger, Jul 04 2019 *)
PROG
(PARI) a(n)={if(n>1, factor(A001008(n))[1, 1], 1)}
CROSSREFS
Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308970 (smallest prime factor) of A001008(n).
Sequence in context: A242223 A308969 A308970 * A120299 A341217 A094900
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jul 03 2019
STATUS
approved