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A072456 Annihilating primes for A000522.

%I A072456 #20 May 15 2020 06:43:07
%S A072456 3,7,11,17,47,53,61,67,73,79,89,101,139,151,157,191,199,229,233,241,
%T A072456 263,269,277,283,311,317,337,347,359,367,379,397,433,449,467,487,503,
%U A072456 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 A072456 Annihilating primes for A000522.
%C A072456 Primes p such that A072453(p) = 0.
%H A072456 Amiram Eldar, <a href="/A072456/b072456.txt">Table of n, a(n) for n = 1..3000</a>
%H A072456 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 A072456 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 A072456 Wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_prime_numbers#Annihilating_primes">Annihilating primes</a>
%o A072456 (Perl) use warnings;
%o A072456   use strict;
%o A072456   use ntheory ":all";
%o A072456   use Math::GMPz;
%o A072456   use Memoize;  memoize 'a000522';
%o A072456   sub a000522 {
%o A072456     my($n, $sum, $fn) = (shift, 0, Math::GMPz->new(1));
%o A072456     do {  $sum += $fn;  $fn *= ($n-$_);  } for 0 .. $n;
%o A072456     $sum;
%o A072456   }
%o A072456   sub a072453 {
%o A072456     my $n = shift;
%o A072456     vecsum( map { a000522($_) % $n == 0 } 0 .. $n-1 );
%o A072456   }
%o A072456   forprimes { print "$_\n" unless a072453($_) } 1000;
%o A072456 # _Dana Jacobsen_, Feb 16 2016
%Y A072456 Cf. A000522, A072453.
%K A072456 nonn
%O A072456 1,1
%A A072456 _N. J. A. Sloane_, Aug 02 2002
%E A072456 More terms from _Vladeta Jovovic_, Aug 02 2002
%E A072456 Offset corrected by _Amiram Eldar_, May 15 2020