A389465 Number of natural numbers in range [n .. sigma(n)] that are coprime to n.

1, 1, 1, 2, 1, 2, 1, 4, 3, 3, 1, 5, 1, 4, 5, 8, 1, 7, 1, 9, 7, 6, 1, 12, 5, 7, 9, 12, 1, 11, 1, 16, 9, 9, 10, 19, 1, 10, 11, 20, 1, 15, 1, 18, 18, 12, 1, 25, 7, 18, 13, 21, 1, 22, 13, 27, 15, 15, 1, 29, 1, 16, 24, 32, 15, 23, 1, 27, 17, 26, 1, 41, 1, 19, 27, 30, 16, 28, 1, 42, 27, 21, 1, 40, 18, 22, 21, 42, 1, 39

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n).

Formula

a(n) = Sum_{k=n..sigma(n)} [1==gcd(k,n)], where [ ] is the Iverson bracket.

a(n) = A389464(n) + A325964(n).

Mathematica

A389465[n_] := Sum[Boole[CoprimeQ[k, n]], {k, n, DivisorSigma[1, n]}];
Array[A389465, 100] (* Paolo Xausa, Oct 11 2025 *)

Prog

(PARI) A389465(n) = sum(k=n, sigma(n), 1==gcd(k, n));

Crossrefs

Cf. A000203, A325964, A389464.

Row lengths of A389466.

Sequence in context: A138567 A103530 A090924 * A247074 A160595 A105778

Adjacent sequences: A389462 A389463 A389464 * A389466 A389467 A389468

Keyword

nonn

Author

Antti Karttunen, Oct 10 2025

Status

approved