A066048 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS

Cf. A000040, A001358, A001248, A000961.

Cf. A130064, A130065.

Sequence in context: A291645 A340769 A088377 * A103164 A210966 A300516

Adjacent sequences: A066045 A066046 A066047 * A066049 A066050 A066051

KEYWORD

nonn,nice,easy

AUTHOR

Reinhard Zumkeller

EXTENSIONS

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

STATUS

approved