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A351605
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a(n) = n^7 * Sum_{d^2|n} 1 / d^7.
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11
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1, 128, 2187, 16512, 78125, 279936, 823543, 2113536, 4785156, 10000000, 19487171, 36111744, 62748517, 105413504, 170859375, 270548992, 410338673, 612499968, 893871739, 1290000000, 1801088541, 2494357888, 3404825447, 4622303232, 6103593750, 8031810176, 10465136172
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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^7*(p^(7*e) - p^(7*floor((e-1)/2)))/(p^7 - 1). - Sebastian Karlsson, Feb 25 2022
Sum_{k=1..n} a(k) ~ c * n^8, where c = zeta(9)/8 = 0.125251... . - Amiram Eldar, Nov 13 2022
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MATHEMATICA
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f[p_, e_] := p^7*(p^(7*e) - p^(7*Floor[(e - 1)/2]))/(p^7 - 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^7*sumdiv(n, d, if (issquare(d), 1/sqrtint(d^7))); \\ 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), this sequence (k=7), A351606 (k=8), A351607 (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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