A322373 Let d_i be the i-th divisor of n. Then a(n) is the largest k such that gcd(d_k, ..., d_tau(n)) = 1.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 1, 3, 1, 5, 1, 1, 2, 2, 2, 4, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 3, 1, 2, 2, 3, 1, 2, 2, 4, 2, 2, 1, 8, 1, 2, 3, 1, 2, 4, 1, 3, 2, 5, 1, 6, 1, 2, 2, 3, 2, 4, 1, 4, 1, 2, 1, 7, 2, 2, 2, 4, 1, 7, 2, 3, 2, 2, 2, 3, 1

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..25200

Example

a(24) = 3 because the divisors of 24 are (1, 2, 3, 4, 6, 8, 12, 24) and from the fourth divisor onwards, d_i is divisible by 2 > 1 but d_3 = 3 is not so a(24) = 3.

Mathematica

Array[LengthWhile[#, # == 1 &] &@ Reverse@ FoldList[GCD[#1, #2] &, Reverse@ Divisors@ #] &, 105] (* Michael De Vlieger, Dec 31 2018 *)

Prog

(PARI) a(n) = my(d=divisors(n), start = max(1, #d-1), g=d[start], i=start); while(g>1, start--; g=gcd(g, d[start])); start

Crossrefs

Cf. A000005, A322374 (positions of records).

Sequence in context: A123529 A140747 A330757 * A332288 A335450 A324191

Adjacent sequences: A322370 A322371 A322372 * A322374 A322375 A322376

Keyword

nonn

Author

David A. Corneth, Dec 09 2018

Status

approved