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 A002791 a(n) = Sum_{d|n, d <= 4} d^2 + 4*Sum_{d|n, d>4} d. (Formerly M3798 N1550) 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)