OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
From Antti Karttunen, Sep 10 2017: (Start)
For n=1, tau(1) = sigma(1) = 1, thus a(1) = 1.
For n=2, tau(2) = 2 & sigma(2) = 3, thus a(2) = 2 + 3 = 5
For n=3, tau(3) = 2 & sigma(3) = 4, thus a(3) = 2 + 3 + 4 = 9.
For n=4, tau(4) = 3 & sigma(4) = 7, thus a(4) = 3 + 4 + 5 + 6 + 7 = 25. (End)
MAPLE
A000217 := proc(n) n*(n+1) /2; end: A162907 := proc(n) A000217(numtheory[sigma](n)) - A000217(numtheory[tau](n)-1) ; end: seq(A162907(n), n=1..100) ; # R. J. Mathar, Jul 21 2009
# second Maple program:
with(numtheory):
a:= n-> ((u, o)-> (u+o)*(o-u+1)/2)(tau(n), sigma(n)):
seq(a(n), n=1..80); # Alois P. Heinz, Sep 10 2017
MATHEMATICA
a[n_] := Range[DivisorSigma[0, n], DivisorSigma[1, n]] // Total;
Array[a, 100] (* Jean-François Alcover, Nov 20 2020 *)
PROG
(PARI)
A000217(n) = n * (n + 1) / 2;
A162907(n) = (A000217(sigma(n)) - A000217(numdiv(n)-1)); \\ Antti Karttunen, Sep 10 2017, after the Maple-code.
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Jul 17 2009
EXTENSIONS
Approximately half of the entries corrected by R. J. Mathar, Jul 21 2009
STATUS
approved