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A332654 a(n) = Sum_{k=1..n} (k/gcd(n, k))^2. 1
1, 2, 6, 12, 31, 33, 92, 96, 165, 172, 386, 239, 651, 499, 656, 776, 1497, 846, 2110, 1262, 1903, 2037, 3796, 1867, 4181, 3408, 4530, 3673, 7715, 3183, 9456, 6232, 7761, 7754, 10062, 6248, 16207, 10889, 12980, 9906, 22141, 9308, 25586, 15027, 17075, 19483, 33512, 14851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse Moebius transform of A053818.

LINKS

Table of n, a(n) for n=1..48.

FORMULA

a(n) = Sum_{k=1..n} (lcm(n, k)/n)^2.

a(n) = Sum_{d|n} Sum_{k=1..d, gcd(k, d) = 1} k^2.

MATHEMATICA

Table[Sum[(k/GCD[n, k])^2, {k, 1, n}], {n, 1, 48}]

Table[Sum[Sum[If[GCD[k, d] == 1, k^2, 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 48}]

PROG

(MAGMA) [&+[(k div Gcd(n, k))^2:k in [1..n]]:n in [1..50]]; // Marius A. Burtea, Feb 18 2020

CROSSREFS

Cf. A053818, A057661, A068963, A069097, A320941, A332655.

Sequence in context: A335287 A322804 A163087 * A000650 A304961 A032178

Adjacent sequences:  A332651 A332652 A332653 * A332655 A332656 A332657

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 18 2020

STATUS

approved

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Last modified April 11 06:00 EDT 2021. Contains 342886 sequences. (Running on oeis4.)