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

1,2

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.

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 *)

Prog

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

Crossrefs

Cf. A000961, A306264.

Sequence in context: A034699 A354933 A346596 * A309639 A327393 A376368

Adjacent sequences: A324385 A324386 A324387 * A324389 A324390 A324391

Keyword

nonn

Author

Antti Karttunen and David James Sycamore, Feb 28 2019

Status

approved