%I M3798 N1550 #34 Aug 17 2019 15:48:44

%S 1,5,10,21,21,38,29,53,46,65,45,102,53,89,90,117,69,146,77,161,122,

%T 137,93,230,121,161,154,217,117,278,125,245,186,209,189,354,149,233,

%U 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

%N a(n) = Sum_{d|n, d <= 4} d^2 + 4*Sum_{d|n, d>4} d.

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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Amiram Eldar, <a href="/A002791/b002791.txt">Table of n, a(n) for n = 1..10000</a>

%H P. A. MacMahon, <a href="https://archive.org/stream/messengerofmathe52cambuoft#page/112/mode/2up">The connexion between the sum of the squares of the divisors and the number of partitions of a given number</a>, Messenger Math., 54 (1924), 113-116.

%F 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

%F 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

%p with(numtheory):

%p A:=proc(s,n) local d,s1,s2;

%p s1:=0; s2:=0;

%p for d in divisors(n) do

%p if d <= s then s1:=s1+d^2 else s2:=s2+d; fi; od:

%p s1+s*s2; end;

%p f:=s->[seq(A(s,n),n=1..80)];

%p f(4);

%t a[n_] := DivisorSum[n, #^2 &, # < 5 &] + 4 * DivisorSum[n, # &, # > 4 &]; Array[a, 70] (* _Amiram Eldar_, Aug 17 2019 *)

%Y Cf. A002659, A002660.

%Y A row of the array in A242639.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Edited by _N. J. A. Sloane_, May 21 2014