A308971 - OEIS

A308971

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

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

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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

Amiram Eldar, Table of n, a(n) for n = 1..325

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. A001008, A006530.

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

Adjacent sequences: A308968 A308969 A308970 * A308972 A308973 A308974

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jul 03 2019

STATUS

approved