A072356 a(n) = if n=p*q^2 for primes p<>q then q*p^2 else n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 13, 14, 15, 16, 17, 12, 19, 50, 21, 22, 23, 24, 25, 26, 27, 98, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 242, 75, 46, 47, 48, 49, 20, 51, 338, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 147, 64, 65, 66, 67, 578, 69, 70, 71

Offset

1,2

Comments

a(a(n))=n: a self-inverse permutation of natural numbers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Maple

N:= 100: # to get a(1) to a(N)
Ps:= select(isprime, [$1..N/2]):
Qs:= select(`<=`, Ps, floor(sqrt(N/2))):
A:= <($1..N)>:
for p in Ps do
  for q in Qs do
    if p*q^2 <= N then A[p*q^2]:= q*p^2 fi
  od
od:
convert(A, list); # Robert Israel, Mar 08 2016

Mathematica

Table[If[Sort[(ar = Transpose[FactorInteger[n]])[[2]]] == {1, 2}, Times @@ (Reverse[ar[[1]]]^ar[[2]]), n], {n, 71}] (* Ivan Neretin, Jul 09 2015 *)

Crossrefs

Cf. A054753.

Sequence in context: A004840 A254650 A032994 * A105119 A069799 A225891

Adjacent sequences: A072353 A072354 A072355 * A072357 A072358 A072359

Keyword

nonn

Author

Reinhard Zumkeller, Jul 18 2002

Status

approved