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A064949
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a(n) = Sum_{i|n, j|n} min(i,j).
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1
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1, 5, 6, 15, 8, 32, 10, 37, 23, 42, 14, 100, 16, 52, 52, 83, 20, 125, 22, 132, 64, 72, 26, 252, 45, 82, 76, 162, 32, 286, 34, 177, 88, 102, 88, 397, 40, 112, 100, 336, 44, 352, 46, 222, 208, 132, 50, 572, 75, 239, 124, 252, 56, 416, 120, 414, 136, 162, 62, 916, 64
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{i=1..tau(n)} (2*tau(n)-2*i+1)*d_i, where {d_i}, i=1..tau(n), is increasing sequence of divisors of n.
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EXAMPLE
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a(6) = dot_product(7,5,3,1)*(1,2,3,6) = 7*1 + 5*2 + 3*3 + 1*6 = 32.
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MAPLE
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with(numtheory): seq(add((2*tau(n)-2*i+1)*sort(convert(divisors(n), 'list'))[i], i=1..tau(n)), n=1..200);
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MATHEMATICA
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Array[Function[{t, d}, Total@ MapIndexed[#1 (2 t - 2 First[#2] + 1) &, d]] @@ {DivisorSigma[0, #], Divisors[#]} &, 61] (* Michael De Vlieger, Oct 25 2021 *)
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PROG
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(PARI) { for (n=1, 1000, d=divisors(n); t=length(d); a=sum(i=1, t, (2*t - 2*i + 1)*d[i]); write("b064949.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 01 2009
(PARI) A064949(n) = { my(i=0, u=numdiv(n)); sumdiv(n, d, i++; (((2*u)-(2*i))+1)*d); }; \\ Antti Karttunen, Nov 14 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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