A389464 Number of natural numbers in range [n .. sigma(n)-1] that are coprime to n.

0, 0, 0, 1, 0, 2, 0, 3, 2, 3, 0, 5, 0, 4, 5, 7, 0, 7, 0, 9, 6, 6, 0, 12, 4, 7, 8, 12, 0, 11, 0, 15, 9, 9, 9, 18, 0, 10, 10, 20, 0, 15, 0, 18, 18, 12, 0, 25, 6, 17, 13, 21, 0, 22, 12, 27, 14, 15, 0, 29, 0, 16, 23, 31, 14, 23, 0, 27, 17, 26, 0, 41, 0, 19, 26, 30, 15, 28, 0, 42, 26, 21, 0, 40, 17, 22, 21, 42, 0, 39

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n).

Formula

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

a(n) = A389465(n) - A325964(n).

Mathematica

A389464[n_] := Sum[Boole[CoprimeQ[k, n]], {k, n, DivisorSigma[1, n] - 1}];
Array[A389464, 100] (* Paolo Xausa, Oct 11 2025 *)

Prog

(PARI) A389464(n) = sum(k=n, sigma(n)-1, 1==gcd(k, n));

Crossrefs

Cf. A000203, A325964, A389465.

Sequence in context: A326689 A334861 A359674 * A323248 A324397 A132623

Adjacent sequences: A389461 A389462 A389463 * A389465 A389466 A389467

Keyword

nonn

Author

Antti Karttunen, Oct 10 2025

Status

approved