A241603 a(n) = Sum_{d|n, d <= 5} d^2 + 5*Sum_{d|n, d>5} d.

1, 5, 10, 21, 26, 44, 36, 61, 55, 80, 56, 120, 66, 110, 110, 141, 86, 179, 96, 196, 150, 170, 116, 280, 151, 200, 190, 266, 146, 344, 156, 301, 230, 260, 236, 435, 186, 290, 270, 436, 206, 464, 216, 406, 380, 350, 236, 600, 281, 455, 350, 476, 266, 584, 356, 586, 390, 440, 296, 820, 306, 470, 510, 621, 416, 704, 336

Offset: 1

Author

N. J. A. Sloane, May 21 2014

Keywords

• nonn

References

• 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. Collected Papers, MIT Press, 1978, Vol. I, pp. 1364-1367.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002659, A002660.

A row of the array in A242639.

Programs

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(5);

Mathematica

sd5[n_]:=Module[{d=Divisors[n]},Total[Select[d,#<6&]^2]+5Total[Select[ d,#>5&]]]; Array[sd5,70] (* Harvey P. Dale, Mar 18 2015 *)

Extensions

Typo in definition corrected by N. J. A. Sloane, Mar 18 2015