OFFSET
1,2
COMMENTS
Also numerator of the sum of all matrix elements of n X n matrix M[i,j] = i/j, i,j=1..n.
p^3 divides a(p-1) for prime p>3, p^3 divides a(p^2-1) for prime p>3, p^3 divides a(p^3-1) for prime p>3, p^3 divides a(p^4-1) for prime p>3, ...
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
MAPLE
a:= n-> numer(add(add(i/j, j=1..n), i=1..n)): seq(a(n), n=1..30); # Zerinvary Lajos, Jun 14 2007
# second Maple program:
h:= proc(n) h(n):= 1/n +`if`(n=1, 0, h(n-1)) end:
t:= proc(n) t(n):= n +`if`(n=1, 0, t(n-1)) end:
a:= n-> numer(h(n)*t(n)):
seq(a(n), n=1..30); # Alois P. Heinz, May 24 2013
MATHEMATICA
Numerator[Table[n(n+1)/2*Sum[1/i, {i, 1, n}], {n, 1, 50}]]. Numerator[Table[Sum[Sum[i/j, {i, 1, n}], {j, 1, n}], {n, 1, 50}]].
Table[(n(n+1))/2 HarmonicNumber[n], {n, 30}]//Numerator (* Harvey P. Dale, May 06 2018 *)
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jun 25 2006, Jul 12 2006
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007
STATUS
approved