A058274 - OEIS

%I #8 Jan 14 2023 08:45:53

%S 1,7,17,39,57,111,131,220,260,379,403,642,611,870,944,1244,1193,1729,

%T 1575,2200,2168,2679,2538,3645,3182,4063,4048,5051,4530,6284,5352,

%U 7037,6674,7939,7434,10035,8329,10482,10125,12500,10765,14427

%N An approximation to sigma_{5/2}(n): ceiling( sum_{d|n} d^(5/2) ).

%H Amiram Eldar, <a href="/A058274/b058274.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) ~ (2/7)*zeta(7/2) * n^(7/2). - _Amiram Eldar_, Jan 14 2023

%p f := proc(n) local d, t1, t2; t2 := 0; t1 := divisors(n); for d in t1 do t2 := t2 + d^(5/2) end do; t2; end proc; # exact value of sigma_{5/2}(n)

%t a[n_] := Ceiling[DivisorSigma[5/2, n]]; Array[a, 50] (* _Amiram Eldar_, Jan 14 2023 *)

%Y Cf. A000203, A001157, A058272, A058273, A261804.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 08 2000