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A346759
a(n) = Sum_{d|n} floor(d^2/4).
2
0, 1, 2, 5, 6, 12, 12, 21, 22, 32, 30, 52, 42, 62, 64, 85, 72, 113, 90, 136, 124, 152, 132, 212, 162, 212, 204, 262, 210, 324, 240, 341, 304, 362, 324, 477, 342, 452, 424, 552, 420, 624, 462, 640, 590, 662, 552, 852, 612, 813, 724, 892, 702, 1024, 792, 1062, 904, 1052, 870, 1364
OFFSET
1,3
COMMENTS
Inverse Moebius transform of quarter-squares (A002620).
LINKS
FORMULA
G.f.: Sum_{k>=1} x^(2*k) / ((1 + x^k) * (1 - x^k)^3).
a(n) = (A001157(n) - A001227(n)) / 4.
MAPLE
f:= proc(n) local d;
add(floor(d^2/4), d=numtheory:-divisors(n))
end proc:
map(f, [$1..100]); # Robert Israel, Dec 28 2023
MATHEMATICA
Table[Sum[Floor[d^2/4], {d, Divisors[n]}], {n, 1, 60}]
nmax = 60; CoefficientList[Series[Sum[x^(2 k)/((1 + x^k) (1 - x^k)^3), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, d^2\4); \\ Michel Marcus, Aug 03 2021
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved