A072456 Annihilating primes for A000522.

3, 7, 11, 17, 47, 53, 61, 67, 73, 79, 89, 101, 139, 151, 157, 191, 199, 229, 233, 241, 263, 269, 277, 283, 311, 317, 337, 347, 359, 367, 379, 397, 433, 449, 467, 487, 503, 521, 541, 563, 569, 571, 577, 593, 607, 613, 619, 647, 659, 673, 683, 691, 727, 743, 769, 773, 809, 823, 827, 911, 919, 929, 953, 971, 991

Offset: 1

Author

N. J. A. Sloane, Aug 02 2002

Keywords

• nonn

Comments

Primes p such that A072453(p) = 0.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3000
• C. Cobeli and A. Zaharescu, Promenade around Pascal Triangle-Number Motives, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, pp. 73-98. - From _N. J. A. Sloane_, Feb 16 2013
• Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5 (1999) 138-150. (ps, pdf)
• Wikipedia, Annihilating primes

Crossrefs

Cf. A000522, A072453.

Programs

Perl

use warnings;
  use strict;
  use ntheory ":all";
  use Math::GMPz;
  use Memoize;  memoize 'a000522';
  sub a000522 {
    my($n, $sum, $fn) = (shift, 0, Math::GMPz->new(1));
    do {  $sum += $fn;  $fn *= ($n-$_);  } for 0 .. $n;
    $sum;
  }
  sub a072453 {
    my $n = shift;
    vecsum( map { a000522($_) % $n == 0 } 0 .. $n-1 );
  }
  forprimes { print "$\n" unless a072453($) } 1000;
# Dana Jacobsen, Feb 16 2016

Extensions

More terms from Vladeta Jovovic, Aug 02 2002

Offset corrected by Amiram Eldar, May 15 2020