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A287620 a(n) = product, with multiplicity, of the prime numbers appearing at leaf positions in the prime tower factorization of n.

%I A287620 #10 May 30 2017 00:19:18
%S A287620 1,2,3,2,5,6,7,3,2,10,11,6,13,14,15,2,17,4,19,10,21,22,23,9,2,26,3,14,
%T A287620 29,30,31,5,33,34,35,4,37,38,39,15,41,42,43,22,10,46,47,6,2,4,51,26,
%U A287620 53,6,55,21,57,58,59,30,61,62,14,6,65,66,67,34,69,70,71
%N A287620 a(n) = product, with multiplicity, of the prime numbers appearing at leaf positions in the prime tower factorization of n.
%C A287620 The prime tower factorization of a number is defined in A182318.
%C A287620 a(n) <= n.
%C A287620 a(n) = n iff n is squarefree (A005117).
%C A287620 a(n) is noncomposite iff n belongs to A164336.
%C A287620 This sequence is surjective; see A287621 for the least k such that a(k) = n.
%C A287620 For n>1, A001222(a(n)) = A064372(n).
%H A287620 Rémy Sigrist, <a href="/A287620/b287620.txt">Table of n, a(n) for n = 1..10000</a>
%H A287620 Rémy Sigrist, <a href="/A287620/a287620.pdf">Illustration of the first terms</a>
%F A287620 Multiplicative with:
%F A287620 - a(p) = p for any prime p,
%F A287620 - a(p^k) = a(k) for any prime p and k > 1.
%e A287620 See illustration of the first terms in Links section.
%o A287620 (PARI) a(n) = my (f=factor(n)); return (prod(i=1, #f~, if (f[i,2]==1, f[i,1], a(f[i,2]))))
%Y A287620 Cf. A001222, A005117, A064372, A164336, A182318, A287621.
%K A287620 nonn,mult
%O A287620 1,2
%A A287620 _Rémy Sigrist_, May 28 2017