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A276984
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Sum of squares of numbers less than n that do not divide n.
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2
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0, 0, 4, 9, 29, 41, 90, 119, 194, 255, 384, 440, 649, 765, 980, 1155, 1495, 1654, 2108, 2324, 2811, 3185, 3794, 4050, 4874, 5351, 6110, 6664, 7713, 8155, 9454, 10075, 11309, 12235, 13610, 14295, 16205, 17209, 18840, 19930, 22139, 23085, 25584, 26808, 29029, 30861, 33510, 34614, 37974, 39670
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OFFSET
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1,3
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LINKS
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FORMULA
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Dirichlet g.f.: (2 zeta(s-3) + 3*zeta(s-2) + zeta(s-1) - 6*zeta(s-2)*zeta(s))/6.
a(n) = n*(n + 1)*(2*n + 1)/6 - sigma_2(n).
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EXAMPLE
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a(3) = 4 because 3 has 2 divisors {1,3} therefore 1 non-divisor {2} and 2^2 = 4;
a(4) = 9 because 4 has 3 divisors {1,2,4} therefore 1 non-divisor {3} and 3^2 = 9;
a(5) = 29 because 5 has 2 divisors {1,5} therefore 3 non-divisors (2,3,4} and 2^2 + 3^2 + 4^2 = 29, etc.
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MATHEMATICA
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Table[n (n + 1) ((2 n + 1)/6) - DivisorSigma[2, n], {n, 1, 50}]
Table[Total[Complement[Range[n], Divisors[n]]^2], {n, 50}] (* Harvey P. Dale, May 10 2018 *)
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PROG
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(PARI) a(n) = n*(n + 1)*(2*n + 1)/6 - sigma(n, 2); \\ Michel Marcus, Sep 29 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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