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Annihilating primes for A000522.
6

%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