1,2

For n>1 a(n) is the determinant of the (n-1) X (n-1) matrix with elements M[i,j] = Prime[i+1] if i=j and 1 otherwise. (See example lines.) - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006

a(n) is divisible by A120271(n) = Numerator of Sum[ 1/(Prime[k]-1), {k,1,n}]. The quotients are a(n)/A120071(n) = A135212(n) = {1, 1, 2, 4, 8, 576, 1152, 2304, 4608, 18432, 552960, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 23 2007

Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 23 2007, Table of n, a(n) for n = 1..54

a(n)=(p(n)-1)*a(n-1)+A005867(n) - Matthew Vandermast (ghodges14(AT)comcast.net), Jun 06 2004

a(n) = Det[ DiagonalMatrix[ Table[ Prime[i+1]-1, {i, 1, n-1} ] ] + 1 ] for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006

a(2)=3 since 2*3=6 and 2,3,4 have 1 prime factor among (2,3)

3 1 1 1 1 ...

1 5 1 1 1 ...

1 1 7 1 1 ...

1 1 1 11 1 ...

1 1 1 1 13 ...

and so a(2) = 3, a(3) = 3*5 - 1*1 = 14, a(4) = 3*5*7 + 1*1*1 + 1*1*1 - 7*1*1 - 5*1*1 - 3*1*1 = 92, etc.

Table[ Det[ DiagonalMatrix[ Table[ Prime[i+1]-1, {i, 1, n-1} ] ] + 1 ], {n, 1, 20} ] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006

(PARI) a(n)=sum(k=1, prod(i=1, n, prime(i)), if(isprime(gcd(k, prod(i=1, n, prime(i)))), 1, 0))

Cf. A135212, A120271.

Sequence in context: A120056 A125788 A101220 this_sequence A089462 A088342 A074531

Adjacent sequences: A078453 A078454 A078455 this_sequence A078457 A078458 A078459

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 31 2002

a(7) from Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 25 2003

a(8)-a(12) from Matthew Vandermast (ghodges14(AT)comcast.net), Jun 06 2004

More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006