%I #20 May 15 2020 06:43:07
%S 3,7,11,17,47,53,61,67,73,79,89,101,139,151,157,191,199,229,233,241,
%T 263,269,277,283,311,317,337,347,359,367,379,397,433,449,467,487,503,
%U 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
%N Annihilating primes for A000522.
%C Primes p such that A072453(p) = 0.
%H Amiram Eldar, <a href="/A072456/b072456.txt">Table of n, a(n) for n = 1..3000</a>
%H C. Cobeli and A. Zaharescu, <a href="http://rms.unibuc.ro/bulletin/pdf/56-1/PromenadePascalPart1.pdf">Promenade around Pascal Triangle-Number Motives</a>, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, pp. 73-98. - From _N. J. A. Sloane_, Feb 16 2013
%H Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5 (1999) 138-150. (<a href="http://math.berkeley.edu/~halbeis/publications/psf/seq.ps">ps</a>, <a href="http://math.berkeley.edu/~halbeis/publications/pdf/seq.pdf">pdf</a>)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_prime_numbers#Annihilating_primes">Annihilating primes</a>
%o (Perl) use warnings;
%o use strict;
%o use ntheory ":all";
%o use Math::GMPz;
%o use Memoize; memoize 'a000522';
%o sub a000522 {
%o my($n, $sum, $fn) = (shift, 0, Math::GMPz->new(1));
%o do { $sum += $fn; $fn *= ($n-$_); } for 0 .. $n;
%o $sum;
%o }
%o sub a072453 {
%o my $n = shift;
%o vecsum( map { a000522($_) % $n == 0 } 0 .. $n-1 );
%o }
%o forprimes { print "$_\n" unless a072453($_) } 1000;
%o # _Dana Jacobsen_, Feb 16 2016
%Y Cf. A000522, A072453.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 02 2002
%E More terms from _Vladeta Jovovic_, Aug 02 2002
%E Offset corrected by _Amiram Eldar_, May 15 2020