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A351607
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a(n) = n^9 * Sum_{d^2|n} 1 / d^9.
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11
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1, 512, 19683, 262656, 1953125, 10077696, 40353607, 134479872, 387440172, 1000000000, 2357947691, 5169858048, 10604499373, 20661046784, 38443359375, 68853956608, 118587876497, 198369368064, 322687697779, 513000000000, 794280046581, 1207269217792, 1801152661463
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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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Multiplicative with a(p^e) = p^9*(p^(9*e) - p^(9*floor((e-1)/2)))/(p^9 - 1). - Sebastian Karlsson, Mar 03 2022
Sum_{k=1..n} a(k) ~ c * n^10, where c = zeta(11)/10 = 0.100049... . - Amiram Eldar, Nov 13 2022
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MATHEMATICA
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f[p_, e_] := p^9*(p^(9*e) - p^(9*Floor[(e - 1)/2]))/(p^9 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Nov 13 2022 *)
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PROG
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(PARI) a(n) = n^9*sumdiv(n, d, if (issquare(d), 1/sqrtint(d^9))); \\ Michel Marcus, Feb 15 2022
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CROSSREFS
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Sequences of the form n^k * Sum_{d^2|n} 1/d^k for k = 0..10: A046951 (k=0), A340774 (k=1), A351600 (k=2), A351601 (k=3), A351602 (k=4), A351603 (k=5), A351604 (k=6), A351605 (k=7), A351606 (k=8), this sequence (k=9), A351608 (k=10).
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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