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

1,1

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.

Links

Table of n, a(n) for n=1..64.

Formula

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

Example

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).

Sequence in context: A056177 A025199 A213858 * A180968 A191847 A321290

Adjacent sequences: A277989 A277990 A277991 * A277993 A277994 A277995

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2016

Status

approved