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

%I #8 Jan 14 2023 08:45:37

%S 1,4,6,12,12,24,20,34,33,47,37,73,48,75,75,98,71,127,84,144,121,144,

%T 111,213,137,183,173,231,157,289,174,279,232,272,238,393,226,321,297,

%U 420,264,463,283,443,404,426,323,610,363,525,441,566,387

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

%H Amiram Eldar, <a href="/A058270/b058270.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_] := Round[DivisorSigma[3/2, n]]; Array[a, 50] (* _Amiram Eldar_, Jan 14 2023 *)

%Y Cf. A000203, A001157, A058269, A058271, A247041.

%K nonn

%O 1,2

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