

A025529


a(n) = (1/1 + 1/2 + ... + 1/n)*lcm{1,2,...,n}.


18



1, 3, 11, 25, 137, 147, 1089, 2283, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, 2436559, 42142223, 42822903, 825887397, 837527025, 848612385, 859193865, 19994251455, 20217344325, 102157567401, 103187226801, 312536252003, 315404588903, 9227046511387
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OFFSET

1,2


COMMENTS

First column of A027446.  Eric Desbiaux, Mar 29 2013
From Amiram Eldar and Thomas Ordowski, Aug 07 2019: (Start)
By Wolstenholme's theorem, if p > 3 is a prime, then p^2  a(p1).
Conjecture: for n > 3, if n^2  a(n1), then n is a prime.
Note that if n = p^2 with prime p > 3, then n  a(n1).
It seems that composite numbers n such that n  a(n1) are only the squares n = p^2 of primes p > 3.
Primes p such that p^3  a(p1) are the Wolstenholme primes A088164.
The nth triangular number n(n+1)/2  a(n) for n = 1, 2, 6, 4422, ... (End)


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Frank A. Haight, and Robert B. Jones., "A probabilistic treatment of qualitative data with special reference to word association tests." Journal of Mathematical Psychology 11.3 (1974): 237244. [Denominators of fractions in Eq. 21.] [Annotated scanned copy]
Frank A. Haight and N. J. A. Sloane, Correspondence, 1975
Yilmaz Simsek, Derivation of Computational Formulas for certain class of finite sums: Approach to Generating functions arising from padic integrals and special functions, arXiv:2108.10756 [math.NT], 2021.


FORMULA

a(n) = A001008(n)*A110566(n).  Arkadiusz Wesolowski, Mar 29 2012
a(n) = Sum_{k=1..n} lcm(1,2,...,n)/k.  Thomas Ordowski, Aug 07 2019


MAPLE

a:= n> add(1/k, k=1..n)*ilcm($1..n):
seq(a(n), n=1..30); # Alois P. Heinz, Mar 14 2013


MATHEMATICA

Table[HarmonicNumber[n]*LCM @@ Range[n], {n, 27}] (* Arkadiusz Wesolowski, Mar 29 2012 *)


PROG

(GAP) List([1..30], n>Sum([1..n], k>1/k)*Lcm([1..n])); # Muniru A Asiru, Apr 02 2018
(PARI) a(n) = sum(k=1, n, 1/k)*lcm([1..n]); \\ Michel Marcus, Apr 02 2018
(Magma) [HarmonicNumber(n)*Lcm([1..n]):n in [1..30]]; // Marius A. Burtea, Aug 07 2019


CROSSREFS

Differs from A096617 at 7th term.
Cf. A001008, A002805, A027446, A110566.
Sequence in context: A001008 A231606 A096617 * A124078 A096795 A160039
Adjacent sequences: A025526 A025527 A025528 * A025530 A025531 A025532


KEYWORD

nonn


AUTHOR

Clark Kimberling


STATUS

approved



