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If n = i^2 * A005117(j) for some i, j > 0 then a(n) = j^2 * A005117(i).
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%I #11 Jul 17 2024 11:42:28

%S 1,4,9,2,16,25,36,8,3,49,64,18,81,100,121,5,144,12,169,32,196,225,256,

%T 50,6,289,27,72,324,361,400,20,441,484,529,7,576,625,676,98,729,784,

%U 841,128,48,900,961,45,10,24,1024,162,1089,75,1156,200,1225,1296

%N If n = i^2 * A005117(j) for some i, j > 0 then a(n) = j^2 * A005117(i).

%C This sequence is a self-inverse permutation of the positive integers with infinitely many fixed points.

%H Rémy Sigrist, <a href="/A374600/b374600.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A374600/a374600.gp.txt">PARI program</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(A249327(n, k)) = A249327(k, n).

%F a(n) = n iff n = k^2 * A005117(k) for some k > 0.

%e For n = 84: 84 = 2^2 * A005117(14), so a(84) = 14^2 * A005117(2) = 392.

%o (PARI) \\ See Links section.

%Y See A374611 for a similar sequence.

%Y Cf. A000188, A005117, A007913, A249327.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jul 13 2024