|
%I #28 Nov 14 2022 01:39:26
%S 1,32,243,1056,3125,7776,16807,33792,59292,100000,161051,256608,
%T 371293,537824,759375,1082368,1419857,1897344,2476099,3300000,4084101,
%U 5153632,6436343,8211456,9768750,11881376,14407956,17748192,20511149,24300000,28629151,34635776,39135393
%N a(n) = n^5 * Sum_{d^2|n} 1 / d^5.
%H Seiichi Manyama, <a href="/A351603/b351603.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p^5*(p^(5*e) - p^(5*floor((e-1)/2)))/(p^5 - 1). - _Sebastian Karlsson_, Feb 25 2022
%F Sum_{k=1..n} a(k) ~ c * n^6, where c = zeta(7)/6 = 0.168058... . - _Amiram Eldar_, Nov 13 2022
%t f[p_, e_] := p^5*(p^(5*e) - p^(5*Floor[(e - 1)/2]))/(p^5 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* _Amiram Eldar_, Nov 13 2022 *)
%o (PARI) a(n) = n^5*sumdiv(n, d, if (issquare(d), 1/sqrtint(d^5))); \\ _Michel Marcus_, Feb 15 2022
%Y 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), this sequence (k=5), A351604 (k=6), A351605 (k=7), A351606 (k=8), A351607 (k=9), A351608 (k=10).
%Y Cf. A013665.
%K nonn,mult
%O 1,2
%A _Wesley Ivan Hurt_, Feb 14 2022
|
