login
An approximation to sigma_{3/2}(n): floor( sum_{d|n} d^(3/2) ).
4

%I #8 Jan 14 2023 08:45:33

%S 1,3,6,11,12,23,19,34,33,46,37,73,47,74,75,98,71,127,83,144,120,143,

%T 111,213,137,183,173,230,157,288,173,279,232,272,237,392,226,320,296,

%U 419,263,463,282,443,404,426,323,610,362,525,440,566,386

%N An approximation to sigma_{3/2}(n): floor( sum_{d|n} d^(3/2) ).

%H Amiram Eldar, <a href="/A058269/b058269.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) ~ (2/5)*zeta(5/2) * n^(5/2). - _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^(3/2) end do; t2; end proc; # exact value of sigma_{3/2}(n)

%t a[n_] := Floor[DivisorSigma[3/2, n]]; Array[a, 50] (* _Amiram Eldar_, Jan 14 2023 *)

%Y Cf. A000203, A001157, A058270, A058271, A247041.

%K nonn

%O 1,2

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