A030664 Product of largest prime <= n and smallest prime >= n.

1, 1, 4, 9, 15, 25, 35, 49, 77, 77, 77, 121, 143, 169, 221, 221, 221, 289, 323, 361, 437, 437, 437, 529, 667, 667, 667, 667, 667, 841, 899, 961, 1147, 1147, 1147, 1147, 1147, 1369, 1517, 1517, 1517, 1681, 1763, 1849, 2021, 2021, 2021, 2209, 2491, 2491, 2491

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice

Comments

Symmetrical about zero, a(n)=a(-n) if n>1, if negative primes are recognized. - Robert G. Wilson v, Feb 28 2011

Iff n is a prime then a(n)=n^2, otherwise a(n) is a semiprime. - Robert G. Wilson v, Feb 28 2011

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A013638, A006094, A001248.

Cf. A007917, A007918, A013638.

Programs

Haskell

a030664 n = a007917 n * a007918 n -- Reinhard Zumkeller, May 22 2015, Feb 24 2011

Mathematica

f[n_] := If[Abs[n] < 2, 1, NextPrime[n + 1, -1] NextPrime[n - 1]]; Array[f, 51, 0] (* Robert G. Wilson v, Feb 28 2011 *)

MuPAD

numlib::prevprime(i)*nextprime(i) $ i = 0..50 // Zerinvary Lajos, Feb 26 2007

PARI

a(n) = if (n < 2, 1, precprime(n)*nextprime(n)); \\ Michel Marcus, Mar 21 2015

Formula

For n > 1: a(n) = A007917(n)*A007918(n). - Reinhard Zumkeller, May 22 2015

Extensions

More terms from Erich Friedman