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A238981
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Sum of n-th powers of unitary divisors of n (d such that d divides n, gcd(d, n/d) = 1).
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3
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1, 5, 28, 257, 3126, 47450, 823544, 16777217, 387420490, 10009766650, 285311670612, 8916117756914, 302875106592254, 11112685048647250, 437893920912786408, 18446744073709551617, 827240261886336764178, 39346558169931834836690, 1978419655660313589123980
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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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MATHEMATICA
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a[n_, k_] := Sum[If[GCD[i, n] == i && GCD[i, n/i] == 1, i^k, 0], {i, n}]; Table[a[n, n], {n, 1, 24}]
a[1] = 1; a[n_] := Times @@ (1 + First[#]^(n * Last[#]) &/@ FactorInteger[n]); Array[a, 19] (* Amiram Eldar, Aug 10 2019 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d^n*(gcd(d, n/d) == 1)); \\ Michel Marcus, Mar 19 2014
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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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