A102440 Replace each prime factor of n that is greater than 3 with the greatest semiprime less than it.

1, 2, 3, 4, 4, 6, 6, 8, 9, 8, 10, 12, 10, 12, 12, 16, 15, 18, 15, 16, 18, 20, 22, 24, 16, 20, 27, 24, 26, 24, 26, 32, 30, 30, 24, 36, 35, 30, 30, 32, 39, 36, 39, 40, 36, 44, 46, 48, 36, 32, 45, 40, 51, 54, 40, 48, 45, 52, 58, 48, 58, 52, 54, 64, 40, 60, 65, 60, 66, 48, 69, 72, 69

Offset: 1

Author

Reinhard Zumkeller, Jan 09 2005

Keywords

• nonn
• mult

Examples

			a(99) = a(3*3*11) -> 3*3*[11->2*5] = 3*3*2*5 = 90.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A102415, A102441, A102442, A102443.

Programs

Mathematica

g[p_] := (* greatest semiprime less than prime p *) g[p] = For[k = p - 1, True, k--, If[PrimeOmega[k] == 2, Return[k]]];
a[n_] := Product[{p, e} = pe; If[p <= 3, p, g[p]]^e, {pe, FactorInteger[n]}];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 27 2019 *)

Formula

Multiplicative with prime(i) -> (if i<=2 then prime(i) else A102415(i)).

a(n) <= n and a(n) = n iff n is 3-smooth, see A003586.

A102441(n) = a(a(n)), see A102442, A102443 for iterations.