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A308993 Multiplicative with a(p) = 1 and a(p^e) = p^a(e) for any e > 1 and prime number p. 2

%I #13 Jul 07 2019 13:09:30

%S 1,1,1,2,1,1,1,2,3,1,1,2,1,1,1,4,1,3,1,2,1,1,1,2,5,1,3,2,1,1,1,2,1,1,

%T 1,6,1,1,1,2,1,1,1,2,3,1,1,4,7,5,1,2,1,3,1,2,1,1,1,2,1,1,3,2,1,1,1,2,

%U 1,1,1,6,1,1,5,2,1,1,1,4,9,1,1,2,1,1,1

%N Multiplicative with a(p) = 1 and a(p^e) = p^a(e) for any e > 1 and prime number p.

%C To compute a(n): remove every prime number at leaf position in the prime tower factorization of n (the prime tower factorization of a number is defined in A182318).

%H Rémy Sigrist, <a href="/A308993/b308993.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A308993/a308993.pdf">Illustration of first terms</a>

%F a(n) = 1 iff n is squarefree.

%F a^k(n) = 1 for any k >= A185102(n) (where a^k denotes the k-th iterate of a).

%F a(n)^2 <= n with equality iff n is the square of some cubefree number (n = A004709(k)^2 for some k > 0).

%e See Links sections.

%o (PARI) a(n) = my (f=factor(n)); prod (i=1, #f~, f[i,1]^if (f[i,2]==1, 0, a(f[i,2])))

%Y Cf. A004709, A005117, A182318, A185102.

%K nonn,mult

%O 1,4

%A _Rémy Sigrist_, Jul 04 2019

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)