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A073111 Number of permutations p of (1,2,3,...,n) such that 1^p(1)+2^p(2)+3^p(3)+...+n^p(n) is prime. 0

%I #11 Mar 30 2012 18:58:21

%S 0,2,0,0,35,211,0,0,56204,337661,0,0,454113487

%N Number of permutations p of (1,2,3,...,n) such that 1^p(1)+2^p(2)+3^p(3)+...+n^p(n) is prime.

%C a(4*k)=a(4*k+3)=0

%e For n=3: permutations (1,3,2), (3,1,2), (2,3,1), (2,1,3) are OK since 1^1+2^3+3^2=13, 1^3+2^1+3^2=11, 1^2+2^3+3^1=11 and 1^2+2^1+3^3=13, hence a(3)=4.

%e For n=2: both permutations (1,2), (2,1) are OK since 1^1+2^2=5 and 1^2+2^1=3; hence a(2)=2.

%o (PARI) a(n)=sum(k=1,n!,if(isprime(sum(i=1,n,i^component(numtoperm(n,k),i)))-1,0,1))

%K more,nonn

%O 1,2

%A _Benoit Cloitre_, Aug 19 2002

%E a(10) and a(11) from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 29 2004

%E a(12)-a(13) from _Robert Gerbicz_, Nov 27 2010

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Last modified July 18 03:55 EDT 2024. Contains 374377 sequences. (Running on oeis4.)