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A050462
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a(n) = Sum_{d|n, n/d=1 mod 4} d^3.
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5
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1, 8, 27, 64, 126, 216, 343, 512, 730, 1008, 1331, 1728, 2198, 2744, 3402, 4096, 4914, 5840, 6859, 8064, 9262, 10648, 12167, 13824, 15751, 17584, 19710, 21952, 24390, 27216, 29791, 32768, 35938, 39312, 43218, 46720, 50654, 54872, 59346
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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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Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = Pi^4/192 + A175572/2 = 1.00181129167264... . (End)
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MATHEMATICA
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a[n_] := Total[(n/Select[Divisors@ n, Mod[#, 4] == 1 &])^3]; Array[a, 39] (* Robert G. Wilson v, Mar 26 2015 *)
a[n_] := DivisorSum[n, #^3 &, Mod[n/#, 4] == 1 &]; Array[a, 50] (* Amiram Eldar, Nov 05 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, ((n/d % 4)== 1)* d^3); \\ Michel Marcus, Mar 26 2015
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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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EXTENSIONS
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STATUS
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approved
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