A277992 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.

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, 52, 53, 55, 56, 58, 65, 67, 70, 71, 76, 77, 80, 83, 85, 88, 91, 92, 97, 98, 100, 101, 107, 113, 115, 116, 118, 121, 122, 127, 130, 133, 136, 137, 140, 142, 143, 148, 155, 157

Offset: 1

Author

Seiichi Manyama, Nov 07 2016

Keywords

• nonn

Comments

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

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

Examples

			a(1) = b(1, 2) = A014968(2) = 2.
a(2) = b(2, 2) = A277968(2) = c(2, 2) = A000716(2)/3 = 3.
a(3) = b(3, 2) = A277974(2) = c(3, 2) = A023004(2)/5 = 4.
a(4) = b(4, 2) = A160549(2) = c(4, 2) = A023006(2)/7 = 5.
a(5) = b(5, 2) = A277912(2) = c(5, 2) = A023010(2)/11 = 7.
		

Crossrefs

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

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).

Formula

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