A102443 a(n)=b(n, A102442(n)), where b(n,0)=n and b(n,k+1)=A102440(b(n,k)).

1, 2, 3, 4, 4, 6, 6, 8, 9, 8, 8, 12, 8, 12, 12, 16, 12, 18, 12, 16, 18, 16, 16, 24, 16, 16, 27, 24, 16, 24, 16, 32, 24, 24, 24, 36, 24, 24, 24, 32, 24, 36, 24, 32, 36, 32, 32, 48, 36, 32, 36, 32, 36, 54, 32, 48, 36, 32, 32, 48, 32, 32, 54, 64, 32, 48, 32, 48, 48, 48, 48, 72, 48

Offset: 1

Author

Reinhard Zumkeller, Jan 09 2005

Keywords

• nonn
• mult

Comments

a(a(n)) = A102440(a(n)) = a(n).

Completely multiplicative because A102440 is. The conversion of every prime into a 3-smooth number is independent of any other prime. - Andrew Howroyd, Jul 31 2018

Examples

			See A102442.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003586, A102440, A102442.

Programs

Mathematica

g[p_] := (* greatest semiprime less than prime p *) g[p] = For[k = p - 1, True, k--, If[PrimeOmega[k] == 2, Return[k]]];
A102440[n_] := Product[{p, e} = pe; If[p <= 3, p, g[p]]^e, {pe, FactorInteger[n]}];
A102442[n_] := Length[NestWhileList[A102440, n, FactorInteger[#][[-1, 1]] > 3 & ] - 1];
a[n_] := b[n, A102442[n]];
b[n_, 0] := n;
b[n_, k_] := A102440[b[n, k - 1]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 16 2021 *)

PARI

a(n)={while(1, my(f=factor(n)); if(!#select(t->t>3, f[,1]), return(n), n=prod(i=1, #f~, my(p=f[i,1]); while(p>4 && bigomega(p)<>2, p--); p^f[i,2])))} \\ Andrew Howroyd, Jul 31 2018