This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A143356 #12 Aug 21 2022 11:33:52 %S A143356 1,4,6,12,11,23,17,32,29,41,30,66,38,61,61,82,53,104,61,115,92,107,77, %T A143356 170,98,132,124,170,104,216,114,201,158,183,158,287,143,210,193,293, %U A143356 161,318,171,291,266,266,189,418,218,335,269,357,220,426,271,429,309,354,250 %N A143356 A051731 * A006218. %F A143356 Inverse Mobius transform (A051731) of A006218. Row sums of triangle A143355. %F A143356 a(n) = Sum_{i=1..n} tau(i)*A135539(n,i). - _Ridouane Oudra_, Jul 26 2022 %F A143356 a(n) = Sum_{d|n} A006218(d). - _Ridouane Oudra_, Jul 27 2022 %e A143356 a(4) = 12 = sum of row 4 terms of triangle A143355: (7, + 3 + 1 + 1). %e A143356 a(4) = 12 = (1, 1, 0, 1) dot (1, 3, 5, 8) = (1 + 3 + 0 + 8), where (1, 1, 0, 1) = row 4 of A051731 and A006218 = (1, 3, 5, 8, 10, 14,...). %o A143356 (PARI) row(n) = my(d=divisors(n)); vector(n, k, #select(x->(x>=k), d)); \\ A135539 %o A143356 a(n) = my(v=row(n)); sum(i=1, n, numdiv(i)*v[i]); \\ _Michel Marcus_, Jul 26 2022 %Y A143356 Cf. A006218, A051731, A143355. %Y A143356 Cf. A135539. %K A143356 nonn %O A143356 1,2 %A A143356 _Gary W. Adamson_, Aug 10 2008 %E A143356 Corrected typo in A-number in formula; added more terms - _R. J. Mathar_, Jan 19 2009