login
b(n, 2) where b(n, m) is defined by expansion of ((Product_{k>=1} (1 - x^(prime(n)*k))/(1 - x^k)^prime(n)) - 1)/prime(n) in powers of x.
0

%I #16 Nov 14 2016 13:06:15

%S 2,3,4,5,7,8,10,11,13,16,17,20,22,23,25,28,31,32,35,37,38,41,43,46,50,

%T 52,53,55,56,58,65,67,70,71,76,77,80,83,85,88,91,92,97,98,100,101,107,

%U 113,115,116,118,121,122,127,130,133,136,137,140,142,143,148,155,157

%N b(n, 2) where b(n, m) is defined by expansion of ((Product_{k>=1} (1 - x^(prime(n)*k))/(1 - x^k)^prime(n)) - 1)/prime(n) in powers of x.

%C c(n, m) is defined by expansion of (Product_{k>=1} 1/(1 - x^k)^prime(n))/prime(n) in powers of x.

%C b(n, 2) = c(n, 2) for n > 1.

%F a(n) = A098090(n - 1) = (prime(n) + 3)/2 for n > 1.

%e a(1) = b(1, 2) = A014968(2) = 2.

%e a(2) = b(2, 2) = A277968(2) = c(2, 2) = A000716(2)/3 = 3.

%e a(3) = b(3, 2) = A277974(2) = c(3, 2) = A023004(2)/5 = 4.

%e a(4) = b(4, 2) = A160549(2) = c(4, 2) = A023006(2)/7 = 5.

%e a(5) = b(5, 2) = A277912(2) = c(5, 2) = A023010(2)/11 = 7.

%Y Cf. A014968, A277968, A277974, A160549, A277912.

%Y Expansion of Product_{k>=1} 1/(1 - x^k)^prime(n): A000712 (n=1), A000716 (n=2), A023004 (n=3), A023006 (n=4), A023010 (n=5).

%K nonn

%O 1,1

%A _Seiichi Manyama_, Nov 07 2016