A304575 a(n) = Sum_{d|n} #{k < d, k squarefree and relatively prime to d}.

1, 2, 3, 4, 4, 6, 6, 8, 7, 8, 8, 12, 9, 12, 12, 15, 12, 16, 13, 17, 16, 18, 16, 24, 17, 20, 20, 23, 18, 26, 20, 28, 23, 26, 24, 33, 24, 29, 28, 35, 27, 35, 29, 37, 34, 35, 31, 46, 32, 38, 35, 41, 33, 45, 36, 47, 38, 42, 37, 54, 38, 46, 46, 54, 42, 53, 42, 54

Offset

1,2

Comments

Note that a(n) <= n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n} A073311(d) (inverse Moebius transform of A073311). - Amiram Eldar, Nov 21 2024

From Ridouane Oudra, Oct 17 2025: (Start)

a(n) = Sum_{k=1..n} A008966(lcm(n,k)/n).

a(n) = Sum_{k=1..n} A008966(k/gcd(n,k)).

a(p^(2*m)) = 1 + Sum_{i=0..m} A013928(p^(2*i)), for p prime and m >= 0.

a(p^(2*m+1)) = 1 + Sum_{i=0..m} A013928(p^(2*i+1)). (End)

Mathematica

s[n_]:=Length[Select[Range[n], And[SquareFreeQ[#], GCD[n, #]===1]&]];
Table[DivisorSum[n, s], {n, 100}]

Prog

(PARI) a(n) = sumdiv(n, d, #select(k->(issquarefree(k) && (gcd(k, d)==1)), [1..d])); \\ Michel Marcus, May 15 2018

Crossrefs

Cf. A000010, A001221, A005117, A008683, A073311, A111972, A112399, A139555, A265675, A304573, A304575, A304576, A008966, A013928.

Sequence in context: A227683 A321166 A092988 * A296421 A138768 A111939

Adjacent sequences: A304572 A304573 A304574 * A304576 A304577 A304578

Keyword

nonn

Author

Gus Wiseman, May 14 2018

Status

approved