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 A242640 Triangle read by rows: T(s,n) (1 <= s <= n) = Sum_{d|n, d <= s} d^2 + s*Sum_{d|n, d>s} d. 1
 1, 3, 5, 4, 7, 10, 7, 13, 17, 21, 6, 11, 16, 21, 26, 12, 23, 32, 38, 44, 50, 8, 15, 22, 29, 36, 43, 50, 15, 29, 41, 53, 61, 69, 77, 85, 13, 25, 37, 46, 55, 64, 73, 82, 91, 18, 35, 50, 65, 80, 90, 100, 110, 120, 130, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 28, 55, 80, 102, 120, 138, 150, 162, 174, 186, 198, 210 (list; table; 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. See Table I. Note that the entry 53 should be 50. LINKS EXAMPLE Triangle begins: [1] [3, 5] [4, 7, 10] [7, 13, 17, 21] [6, 11, 16, 21, 26] [12, 23, 32, 38, 44, 50] [8, 15, 22, 29, 36, 43, 50] [15, 29, 41, 53, 61, 69, 77, 85] ... The full array (see A242639) begins: 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, ... 1, 5, 7, 13, 11, 23, 15, 29, 25, 35, 23, 55, ... 1, 5, 10, 17, 16, 32, 22, 41, 37, 50, 34, 80, ... 1, 5, 10, 21, 21, 38, 29, 53, 46, 65, 45, 102, ... 1, 5, 10, 21, 26, 44, 36, 61, 55, 80, 56, 120, ... 1, 5, 10, 21, 26, 50, 43, 69, 64, 90, 67, 138, ... 1, 5, 10, 21, 26, 50, 50, 77, 73, 100, 78, 150, ... 1, 5, 10, 21, 26, 50, 50, 85, 82, 110, 89, 162, ... ... 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; for n from 1 to 15 do lprint([seq(A(s, n), s=1..n)]); od: CROSSREFS Upper triangle of array in A242639. Sequence in context: A096457 A277897 A082568 * A210195 A069918 A200700 Adjacent sequences:  A242637 A242638 A242639 * A242641 A242642 A242643 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, May 21 2014 STATUS approved

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)