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

%I A241603 #13 Mar 18 2015 15:31:55
%S A241603 1,5,10,21,26,44,36,61,55,80,56,120,66,110,110,141,86,179,96,196,150,
%T A241603 170,116,280,151,200,190,266,146,344,156,301,230,260,236,435,186,290,
%U A241603 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
%N A241603 a(n) = Sum_{d|n, d <= 5} d^2 + 5*Sum_{d|n, d>5} d.
%D A241603 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.
%H A241603 Harvey P. Dale, <a href="/A241603/b241603.txt">Table of n, a(n) for n = 1..1000</a>
%p A241603 with(numtheory):
%p A241603 A:=proc(s,n) local d,s1,s2;
%p A241603 s1:=0; s2:=0;
%p A241603 for d in divisors(n) do
%p A241603 if d <= s then s1:=s1+d^2 else s2:=s2+d; fi; od:
%p A241603 s1+s*s2; end;
%p A241603 f:=s->[seq(A(s,n),n=1..80)];
%p A241603 f(5);
%t A241603 sd5[n_]:=Module[{d=Divisors[n]},Total[Select[d,#<6&]^2]+5Total[Select[ d,#>5&]]]; Array[sd5,70] (* _Harvey P. Dale_, Mar 18 2015 *)
%Y A241603 Cf. A002659, A002660.
%Y A241603 A row of the array in A242639.
%K A241603 nonn
%O A241603 1,2
%A A241603 _N. J. A. Sloane_, May 21 2014
%E A241603 Typo in definition corrected by _N. J. A. Sloane_, Mar 18 2015