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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A001157, A001227, A002620, A086670, A346758.

Sequence in context: A069789 A332683 A086334 * A198331 A057518 A289206

Adjacent sequences: A346756 A346757 A346758 * A346760 A346761 A346762

Keyword

nonn,look

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved