A066048 Product of smallest and greatest prime factors of n.

1, 4, 9, 4, 25, 6, 49, 4, 9, 10, 121, 6, 169, 14, 15, 4, 289, 6, 361, 10, 21, 22, 529, 6, 25, 26, 9, 14, 841, 10, 961, 4, 33, 34, 35, 6, 1369, 38, 39, 10, 1681, 14, 1849, 22, 15, 46, 2209, 6, 49, 10, 51, 26, 2809, 6, 55, 14, 57, 58, 3481, 10, 3721, 62, 21, 4, 65, 22, 4489, 34

Offset: 1

Author

Reinhard Zumkeller

Keywords

• nonn
• nice
• easy

Comments

For all n > 1, a(n) is semiprime; n is semiprime iff a(n) = n; n is prime iff a(n) = n^2;

For all primes p and k > 0, a(p^k) = p^2.

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A001248, A000961.

Cf. A130064, A130065.

Programs

Mathematica

f[n_] := Transpose[ FactorInteger[n]][[1]]; Table[ First[f[n]]*Last[f[n]], {n, 2, 100} ]
p[n_]:=Module[{fctrs=Transpose[FactorInteger[n]][[1]]},First[fctrs] Last[fctrs]]; Array[p,70] (* Harvey P. Dale, Jun 11 2011 *)

PARI

{ for (n = 1, 10000, if (n==1, a=1, f=factor(n)~; a=f[1, 1] * f[1, length(f)]); write("b066048.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 08 2009

Formula

a(n) = A020639(n) * A006530(n).

Extensions

More terms from Robert G. Wilson v, Jan 03 2002