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%I #29 Oct 14 2022 09:25:06
%S 1,2,3,4,5,9,7,8,9,25,11,18,13,49,25,16,17,27,19,50,49,121,23,36,25,
%T 169,27,98,29,75,31,32,121,289,49,54,37,361,169,100,41,147,43,242,75,
%U 529,47,72,49,125,289,338,53,81,121,196,361,841,59,150,61,961,147,64,169,363
%N a(n) = (n / SmallestPrimeFactor(n)) * GreatestPrimeFactor(n).
%H Reinhard Zumkeller, <a href="/A130064/b130064.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Erdős and J. H. van Lint, <a href="https://doi.org/10.1016/S1385-7258(82)80002-4">On the average ratio of the smallest and largest prime divisor of n</a>, Indagationes Mathematicae (Proceedings), Vol. 85, No. 2 (1982), pp. 127-132.
%F a(n) = n*A006530(n)/A020639(n) = A032742(n)*A006530(n);
%F a(n) >= n.
%F a(n) = n iff n is a prime power: a(A000961(n)) = A000961(n);
%F a(A001221(n)) <= A001221(n); a(A001222(n)) = A001222(n);
%F a(n) = A130065(n)+n*A046665(n)*A074320(n)/A066048(n) = A000290(n)/A130065(n).
%F Sum_{k=1..n} k/a(k) ~ n/log(n) + 3*n/log(n)^2 + o(n/log(n)^2) (Erdős and van Lint, 1982). - _Amiram Eldar_, Oct 14 2022
%t a[n_] := With[{pp = FactorInteger[n][[All, 1]]}, n*pp[[-1]]/pp[[1]]];
%t Array[a, 100] (* _Jean-François Alcover_, Nov 18 2021 *)
%o (PARI) a(n) = if (n==1, 1, my(f=factor(n)[, 1]~); n*vecmax(f)/vecmin(f)); \\ _Michel Marcus_, Sep 24 2022
%o (Python)
%o from sympy import factorint
%o def a(n): f = factorint(n); return 1 if n == 1 else n//min(f)*max(f)
%o print([a(n) for n in range(1, 67)]) # _Michael S. Branicky_, Sep 24 2022
%Y Cf. A006530, A020639, A032742, A000961.
%Y Cf. A001221, A001222.
%Y Cf. A000290, A046665, A074320, A066048, A130065
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, May 05 2007
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