A324388 If n is a prime power (in A000961), then a(n) = n, otherwise a(n) is the greatest proper unitary 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, 15, 31, 32, 11, 17, 7, 9, 37, 19, 13, 8, 41, 21, 43, 11, 9, 23, 47, 16, 49, 25, 17, 13, 53, 27, 11, 8, 19, 29, 59, 20, 61, 31, 9, 64, 13, 33, 67, 17, 23, 35, 71, 9, 73, 37, 25, 19, 11, 39, 79, 16, 81, 41, 83, 28, 17, 43, 29, 11, 89, 45

Offset: 1

Author

Antti Karttunen and David James Sycamore, Feb 28 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14, with a color function showing prime n in red, n that is a proper prime power in gold, n that is composite and squarefree in green, and n that is neither squarefree nor prime power in blue and magenta, where magenta signifies powerful n that is not a prime power.

Crossrefs

Cf. A000961, A306264.

Programs

Mathematica

a[n_] := If[PrimePowerQ[n], n, SelectFirst[Transpose@ {Reverse@ #[[-Ceiling[Length[#]/2] ;; -2]], #[[2 ;; Ceiling[Length[#]/2]]]} &@ Divisors[n], CoprimeQ @@ # &][[1]] ]; a[1] = 1; Array[a, 120] (* Michael De Vlieger, Jun 24 2025 *)

PARI

A324388(n) = if(1>=omega(n),n,fordiv(n,d,if((d>1)&&(1==gcd(d,n/d)),return(n/d))));