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 A132065 a(n) = Sum_{k=1 to d(n)} C(d(n)-1, k-1) d_k, where d(n) is the number of divisors of n and d_k is the k-th divisor of n. 2
 1, 3, 4, 9, 6, 22, 8, 27, 16, 32, 12, 123, 14, 42, 40, 81, 18, 164, 20, 171, 52, 62, 24, 704, 36, 72, 64, 219, 30, 808, 32, 243, 76, 92, 72, 1765, 38, 102, 88, 944, 42, 1016, 44, 315, 276, 122, 48, 4075, 64, 336, 112, 363, 54, 1224, 104, 1170, 124, 152, 60, 17815, 62 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 FORMULA a(p) = p+1, for p prime. - Michel Marcus, Sep 13 2014 EXAMPLE Since the divisors of 12 are 1,2,3,4,6,12 and since row (d(12)-1) of Pascal's triangle is 1,5,10,10,5,1, a(12) = 1*1 + 5*2 + 10*3 + 10*4 + 5*6 + 1*12 = 123. From Peter Luschny, May 18 2016: (Starts) Also the lower vertex of the accumulation triangle of the divisors of n. For instance a(39) = 88 because the lower vertex of ATD(39) = 88. ATD(39) is: [ 39  13  3  1] [ 52  16  4] [ 68  20] [ 88] (End) MATHEMATICA f[n_] := Block[{d, l, k}, d = Divisors[n]; l = Length[d]; Sum[ Binomial[l - 1, k - 1]*d[[k]], {k, l}]]; Array[f, 100] (* Ray Chandler, Oct 31 2007 *) Table[Sum[Binomial[Length[Divisors[n]] - 1, k - 1]*Divisors[n][[k]], {k, 1, Length[Divisors[n]]}], {n, 1, 70}] (* Stefan Steinerberger, Oct 31 2007 *) PROG (PARI) a(n) = {d = divisors(n); sum(i=1, #d, d[i]*binomial(#d-1, i-1)); } \\ Michel Marcus, Sep 13 2014 (Sage) def A132065(n):     D = divisors(n)[::-1]     T = matrix(ZZ, len(D))     for (m, d) in enumerate(D):         T[0, m] = d         for k in range(m-1, -1, -1) :             T[m-k, k] = T[m-k-1, k+1] + T[m-k-1, k]     return T[len(D)-1, 0] print([A132065(n) for n in range(1, 62)]) # Peter Luschny, May 18 2016 CROSSREFS Cf. A007318 (Pascal's triangle), A027750 (divisors of n). Sequence in context: A003959 A168341 A083111 * A157020 A180253 A264786 Adjacent sequences:  A132062 A132063 A132064 * A132066 A132067 A132068 KEYWORD nonn AUTHOR Leroy Quet, Oct 30 2007 EXTENSIONS Extended by Ray Chandler and Stefan Steinerberger, Nov 01 2007 STATUS approved

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Last modified July 10 00:05 EDT 2020. Contains 335570 sequences. (Running on oeis4.)