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

1,2

Links

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

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.

Example

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

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 *)

Crossrefs

Cf. A102415, A102441, A102442, A102443.

Sequence in context: A003962 A102443 A102441 * A372671 A124815 A081328

Adjacent sequences: A102437 A102438 A102439 * A102441 A102442 A102443

Keyword

nonn,mult

Author

Reinhard Zumkeller, Jan 09 2005

Status

approved