

A102440


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


6



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
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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 3smooth, 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] (* JeanFrançois Alcover, Sep 27 2019 *)


CROSSREFS

Cf. A102415, A102441, A102442, A102443.
Sequence in context: A003962 A102443 A102441 * A124815 A081328 A179276
Adjacent sequences: A102437 A102438 A102439 * A102441 A102442 A102443


KEYWORD

nonn,mult


AUTHOR

Reinhard Zumkeller, Jan 09 2005


STATUS

approved



