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A102440 Replace each prime factor of n that is greater than 3 with the greatest semiprime less than it. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..73.

FORMULA

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

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-Fran├žois Alcover, Sep 27 2019 *)

CROSSREFS

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

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Last modified November 12 14:43 EST 2019. Contains 329058 sequences. (Running on oeis4.)