A130065 a(n) = (n / GreatestPrimeFactor(n)) * SmallestPrimeFactor(n).

1, 2, 3, 4, 5, 4, 7, 8, 9, 4, 11, 8, 13, 4, 9, 16, 17, 12, 19, 8, 9, 4, 23, 16, 25, 4, 27, 8, 29, 12, 31, 32, 9, 4, 25, 24, 37, 4, 9, 16, 41, 12, 43, 8, 27, 4, 47, 32, 49, 20, 9, 8, 53, 36, 25, 16, 9, 4, 59, 24, 61, 4, 27, 64, 25, 12, 67, 8, 9, 20, 71, 48, 73, 4, 45, 8, 49, 12, 79, 32, 81

Offset: 1

Author

Reinhard Zumkeller, May 05 2007

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A001221, A001222, A006530, A000961, A020639, A046665, A052126, A066048, A074320, A130064.

Programs

Mathematica

a[n_] := Module[{ps = First /@ FactorInteger[n]}, n * First[ps] / Last[ps]]; Array[a, 100] (* Amiram Eldar, Nov 27 2020 *)

PARI

a(n) = if (n==1, 1, my(f=factor(n)[,1]~); n*vecmin(f)/vecmax(f)); \\ Michel Marcus, Nov 27 2020

Formula

a(n) = n*A020639(n)/A006530(n) = A052126(n)*A020639(n);

a(n) <= n; a(n) = n iff n is a prime power: a(A000961(n)) = A000961(n);

a(A001221(n)) <= A001221(n); a(A001222(n)) = A001222(n);

a(n) = A130064(n) - n*A046665(n)*A074320(n)/A066048(n) = A000290(n)/A130064(n).