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

1,2

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A052128, A076388.

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

Sequence in context: A345993 A330691 A034699 * A346596 A324388 A309639

Adjacent sequences: A354930 A354931 A354932 * A354934 A354935 A354936

Keyword

nonn

Author

Antti Karttunen, Jun 16 2022

Extensions

Definition rewritten by Jianing Song, Sep 28 2022

Status

approved