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a(n) = lcm(A020639(n), A032742(n)).
1

%I #27 Oct 28 2024 09:35:33

%S 1,2,3,2,5,6,7,4,3,10,11,6,13,14,15,8,17,18,19,10,21,22,23,12,5,26,9,

%T 14,29,30,31,16,33,34,35,18,37,38,39,20,41,42,43,22,15,46,47,24,7,50,

%U 51,26,53,54,55,28,57,58,59,30,61,62,21,32,65,66,67,34,69

%N a(n) = lcm(A020639(n), A032742(n)).

%H Paolo Xausa, <a href="/A371573/b371573.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) <= n.

%F a(p) = p, for p prime.

%F Suppose n>1 and p = A020639(n). a(n) = n if p^2 does not divide n and a(n) = n/p otherwise. - _Chai Wah Wu_, Apr 04 2024

%F From _Amiram Eldar_, Oct 28 2024: (Start)

%F a(n) < n if and only if n is in A283050.

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - A283071 + Sum_{p prime} (Product_{primes q < p } (1 - 1/q))/p^3 = 0.8172359231... . (End)

%t Join[{1}, Map[LCM[#[[2]], #[[-2]]] &, Divisors[Range[2, 100]]]]

%o (PARI) a(n) = if (n==1,1, my(x=factor(n)[1,1]); lcm(x, n/x)); \\ _Michel Marcus_, Apr 02 2024

%o (Python)

%o from math import lcm

%o from sympy import factorint

%o def a(n): return 1 if n==1 else lcm((p:=min(factorint(n))), n//p)

%o print([a(n) for n in range(1, 70)]) # _Michael S. Branicky_, Apr 04 2024

%o (Python)

%o from sympy import factorint

%o def A371573(n): return n if (p:=min(factorint(n).items(),default=(1,1)))[1] == 1 else n//p[0] # _Chai Wah Wu_, Apr 04 2024

%Y Cf. A020639, A032742, A088835, A283050, A283071.

%K nonn,easy

%O 1,2

%A _Paolo Xausa_, Mar 30 2024