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A346759 a(n) = Sum_{d|n} floor(d^2/4).

%I A346759 #12 Dec 28 2023 17:35:59
%S A346759 0,1,2,5,6,12,12,21,22,32,30,52,42,62,64,85,72,113,90,136,124,152,132,
%T A346759 212,162,212,204,262,210,324,240,341,304,362,324,477,342,452,424,552,
%U A346759 420,624,462,640,590,662,552,852,612,813,724,892,702,1024,792,1062,904,1052,870,1364
%N A346759 a(n) = Sum_{d|n} floor(d^2/4).
%C A346759 Inverse Moebius transform of quarter-squares (A002620).
%H A346759 Robert Israel, <a href="/A346759/b346759.txt">Table of n, a(n) for n = 1..10000</a>
%F A346759 G.f.: Sum_{k>=1} x^(2*k) / ((1 + x^k) * (1 - x^k)^3).
%F A346759 a(n) = (A001157(n) - A001227(n)) / 4.
%p A346759 f:= proc(n) local d;
%p A346759     add(floor(d^2/4),d=numtheory:-divisors(n))
%p A346759 end proc:
%p A346759 map(f, [$1..100]); # _Robert Israel_, Dec 28 2023
%t A346759 Table[Sum[Floor[d^2/4], {d, Divisors[n]}], {n, 1, 60}]
%t A346759 nmax = 60; CoefficientList[Series[Sum[x^(2 k)/((1 + x^k) (1 - x^k)^3), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A346759 (PARI) a(n) = sumdiv(n, d, d^2\4); \\ _Michel Marcus_, Aug 03 2021
%Y A346759 Cf. A001157, A001227, A002620, A086670, A346758.
%K A346759 nonn,look
%O A346759 1,3
%A A346759 _Ilya Gutkovskiy_, Aug 02 2021