A242643 a(n) = Sum_{d|n, d <= 6} d^2 + 6*Sum_{d|n, d>6} d.

1, 5, 10, 21, 26, 50, 43, 69, 64, 90, 67, 138, 79, 131, 125, 165, 103, 212, 115, 226, 178, 203, 139, 330, 176, 239, 226, 315, 175, 405, 187, 357, 274, 311, 278, 516, 223, 347, 322, 514, 247, 554, 259, 483, 449, 419, 283, 714, 337, 540, 418, 567, 319, 698, 422, 699, 466, 527, 355, 973, 367, 563, 610, 741, 494, 842

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. See Table I. Note that the entry 53 should be 50.

Links

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

Crossrefs

A row of the array in A242641.

Programs

Mathematica

sd6[n_]:=Module[{d=Divisors[n]},Total[Select[d,#<7&]^2]+6Total[Select[ d,#>6&]]];Array[sd6,70] (* Harvey P. Dale, Mar 18 2015 *)

Extensions

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