A371573 a(n) = lcm(A020639(n), A032742(n)).
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, 14, 29, 30, 31, 16, 33, 34, 35, 18, 37, 38, 39, 20, 41, 42, 43, 22, 15, 46, 47, 24, 7, 50, 51, 26, 53, 54, 55, 28, 57, 58, 59, 30, 61, 62, 21, 32, 65, 66, 67, 34, 69
Offset: 1
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Join[{1}, Map[LCM[#[[2]], #[[-2]]] &, Divisors[Range[2, 100]]]] -
PARI
a(n) = if (n==1,1, my(x=factor(n)[1,1]); lcm(x, n/x)); \\ Michel Marcus, Apr 02 2024
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Python
from math import lcm from sympy import factorint def a(n): return 1 if n==1 else lcm((p:=min(factorint(n))), n//p) print([a(n) for n in range(1, 70)]) # Michael S. Branicky, Apr 04 2024
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Python
from sympy import factorint 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
Formula
a(n) <= n.
a(p) = p, for p prime.
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
From Amiram Eldar, Oct 28 2024: (Start)
a(n) < n if and only if n is in A283050.
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)