OFFSET
1,2
REFERENCES
Collected Papers, MIT Press, 1978, Vol. I, pp. 1364-1367.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
P. A. MacMahon, The connexion between the sum of the squares of the divisors and the number of partitions of a given number, Messenger Math., 54 (1924), 113-116.
FORMULA
Conjectured: Inverse Moebius transform of g.f.: (x + 2x^2 + 2x^3 + 2x^4 - 3x^4) / (1 - x)^2. - Sean A. Irvine, May 16 2014
Conjectured: a(n) = 4 * sigma(n) - f(n mod 6) where f(0) = 10, f(1) = 3, f(2) = 7, f(3) = 6, f(4) = 7, f(5) = 3. - Sean A. Irvine, May 17 2014
MAPLE
with(numtheory):
A:=proc(s, n) local d, s1, s2;
s1:=0; s2:=0;
for d in divisors(n) do
if d <= s then s1:=s1+d^2 else s2:=s2+d; fi; od:
s1+s*s2; end;
f:=s->[seq(A(s, n), n=1..80)];
f(4);
MATHEMATICA
a[n_] := DivisorSum[n, #^2 &, # < 5 &] + 4 * DivisorSum[n, # &, # > 4 &]; Array[a, 70] (* Amiram Eldar, Aug 17 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, May 21 2014
STATUS
approved