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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..13.

Example

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.
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.

Prog

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

Crossrefs

Sequence in context: A288125 A020916 A179072 * A229685 A230469 A004076

Adjacent sequences: A073108 A073109 A073110 * A073112 A073113 A073114

Keyword

more,nonn

Author

Benoit Cloitre, Aug 19 2002

Extensions

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

a(12)-a(13) from Robert Gerbicz, Nov 27 2010

Status

approved