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URL: https://oeis.org/A351606

⇱ A351606 - OEIS

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A351606
a(n) = n^8 * Sum_{d^2|n} 1 / d^8.
11
1, 256, 6561, 65792, 390625, 1679616, 5764801, 16842752, 43053282, 100000000, 214358881, 431661312, 815730721, 1475789056, 2562890625, 4311810048, 6975757441, 11021640192, 16983563041, 25700000000, 37822859361, 54875873536, 78310985281, 110505295872, 152588281250
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = p^8*(p^(8*e) - p^(8*floor((e-1)/2)))/(p^8 - 1). - Sebastian Karlsson, Feb 25 2022
Sum_{k=1..n} a(k) ~ c * n^9, where c = zeta(10)/9 = Pi^10/841995 = 0.1112216... . - Amiram Eldar, Nov 13 2022
MATHEMATICA
f[p_, e_] := p^8*(p^(8*e) - p^(8*Floor[(e - 1)/2]))/(p^8 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Nov 13 2022 *)
PROG
(PARI) a(n) = n^8*sumdiv(n, d, if (issquare(d), 1/d^4)); \\ Michel Marcus, Feb 15 2022
CROSSREFS
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), this sequence (k=8), A351607 (k=9), A351608 (k=10).
Cf. A013668.
Sequence in context: A210840 A001016 A352054 * A343288 A050755 A046457
KEYWORD
nonn,mult
AUTHOR
Wesley Ivan Hurt, Feb 14 2022
STATUS
approved