A002791 a(n) = Sum_{d|n, d <= 4} d^2 + 4*Sum_{d|n, d>4} d. (Formerly M3798 N1550)

1, 5, 10, 21, 21, 38, 29, 53, 46, 65, 45, 102, 53, 89, 90, 117, 69, 146, 77, 161, 122, 137, 93, 230, 121, 161, 154, 217, 117, 278, 125, 245, 186, 209, 189, 354, 149, 233, 218, 353, 165, 374, 173, 329, 306, 281, 189, 486, 225, 365, 282, 385, 213, 470, 285, 473, 314, 353, 237, 662, 245, 377, 410, 501, 333, 566, 269, 497

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

Cf. A002659, A002660.

A row of the array in A242639.

Sequence in context: A244026 A244022 A365112 * A080399 A017667 A241603

Adjacent sequences: A002788 A002789 A002790 * A002792 A002793 A002794

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, May 21 2014

Status

approved