1,2

All a(n) are either 1, semiprime or prime. a(n) = 1 for n = 1 and n = {7,13,17,19,24,25,27,31,32,34,37,38,43,45,47,49,...} = A067656 Numbers n such that n!*B(2n) is an integer, where B(2n) are the Bernoulli numbers. p divides a(p-1) for prime p>3. p divides a((p-1)/2) for prime p>3.

a(p-1) = p*(2p-1) is a semiprime hexagonal number for prime p = {7,19,31,37,79,97,139,157,199,211,229,271,307,331,337,367,379,439,499,...} = A005382(n) for n>2, where A005382(n) are the numbers n such that n and 2n-1 are primes.

a(p-1) = p for prime p = {5, 11, 13, 17, 23, 29, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, ...} = Primes that do not belong to A005382(n). a((p-1)/2) = p for prime p = {5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 67, 71, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 259, 271, 281, 283, 293, 307, 311, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 401, ...} that is apparently a union of {5} and A034849(n).

a(n) = Numerator[ Sum[ k^2, {k,1,n} ] / Product[ k^2, {k,1,n} ] ]. a(n) = Numerator[ n(n+1)(2n+1)/6/(n!)^2 ].

Table[Numerator[n(n+1)(2n+1)/6/(n!)^2], {n, 1, 500}]

Cf. A067656, A005382, A034849.

Sequence in context: A065478 A109353 A121595 this_sequence A139428 A063005 A059249

Adjacent sequences: A125291 A125292 A125293 this_sequence A125295 A125296 A125297

nonn,frac

Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 17 2007