A354933 a(1) = 1; for n > 1, a(n) = n / the largest divisor of n that is coprime to a larger divisor of n.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 4, 13, 7, 5, 16, 17, 9, 19, 5, 7, 11, 23, 8, 25, 13, 27, 7, 29, 6, 31, 32, 11, 17, 7, 9, 37, 19, 13, 8, 41, 7, 43, 11, 9, 23, 47, 16, 49, 25, 17, 13, 53, 27, 11, 8, 19, 29, 59, 12, 61, 31, 9, 64, 13, 11, 67, 17, 23, 10, 71, 9, 73, 37, 25, 19, 11, 13, 79, 16, 81, 41, 83, 12, 17, 43

Offset: 1

Author

Antti Karttunen, Jun 16 2022

Keywords

• nonn

Comments

a(n) is the smallest divisor d of n such that d >= sqrt(n) and that gcd(d,n/d) = 1. For the proof see A052128. - Jianing Song, Sep 28 2022

Links

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

Crossrefs

Cf. A052128, A076388.

Differs from A346596 for the first time at n=60, where a(60) = 12, while A346596(60) = 15.

Programs

Mathematica

a[n_] := SelectFirst[Divisors[n], # >= n/# && CoprimeQ[#, n/#] &]; Array[a, 100] (* Amiram Eldar, Jun 16 2022 *)

PARI

A354933(n) = fordiv(n,d,if((d>=(n/d)) && 1==gcd(d,n/d), return(d)));

Formula

a(n) = n / A052128(n).

a(n) = A052128(n) + A076388(n).

Extensions

Definition rewritten by Jianing Song, Sep 28 2022