1,1

p divides a(p) and a(p-1) for prime p. p^2 divides a(p) for prime p = {5, 13, 563, ...} which coincide with known Wilson primes A007540(n) = {5, 13, 563, ...} primes p such that (p-1)! == -1 mod p^2. p^2 divides a(p-1) for prime p = {3, 11, 107, ...} which coincides with the first few known odd primes p such that (p-2)! == 1 mod p^2 and belong to A079853(n) = {2, 3, 11, 107, 4931, ...}.

a(n) = Sum[ i^j, {i,1,n}, {j,1,n} ] + 1. a(n) = Sum[ i*(i^n-1)/(i-1), {i,2,n} ] + n + 1. a(n) = A086787(n) + 1.

Table[Sum[i^j, {i, 1, n}, {j, 1, n}]+1, {n, 1, 20}]

Cf. A086787 = Sum(Sum(i^j, j=1..n), i=1..n). Cf. A079853 = Primes p for which (p-2)! == 1 mod p^2. Cf. A007540 = Wilson primes: primes p such that (p-1)! == -1 mod p^2.

Sequence in context: A004103 A111545 A070075 this_sequence A141787 A047852 A116867

Adjacent sequences: A124402 A124403 A124404 this_sequence A124406 A124407 A124408

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 14 2006