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 A002660 a(n) = Sum_{d|n, d <= 3} d^2 + 3*Sum_{d|n, d>3} d. (Formerly M3797 N1549) 4
 1, 5, 10, 17, 16, 32, 22, 41, 37, 50, 34, 80, 40, 68, 70, 89, 52, 113, 58, 122, 94, 104, 70, 176, 91, 122, 118, 164, 88, 212, 94, 185, 142, 158, 142, 269, 112, 176, 166, 266, 124, 284, 130, 248, 232, 212, 142, 368, 169, 275, 214, 290, 160, 356, 214, 356, 238, 266, 178, 500, 184, 284, 310, 377, 250, 428, 202, 374, 286 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. 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 FORMULA Conjectured: Inverse Moebius transform of g.f.: (x + 2x^2 + 2x^3 - 2x^4) / (1 - x)^2. - Sean A. Irvine, May 16 2014 a(n) = 3 * sigma(n) - k, where k = 4 if n is even and k = 2 if n is odd. - Sean A. Irvine, May 16 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(3); CROSSREFS Cf. A000203, A002659, A002791. A row of the array in A242639. Sequence in context: A152234 A054514 A200940 * A313941 A313942 A050321 Adjacent sequences:  A002657 A002658 A002659 * A002661 A002662 A002663 KEYWORD nonn AUTHOR EXTENSIONS Entry revised by N. J. A. Sloane, May 21 2014 STATUS approved

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Last modified January 18 10:53 EST 2019. Contains 319271 sequences. (Running on oeis4.)