A103729 Column k=2 sequence of array A103728.

1, 5, 13, 41, 61, 113, 145, 221, 365, 421, 613, 761, 841, 1013, 1301, 1625, 1741, 2113, 2381, 2521, 2965, 3281, 3785, 4513, 4901, 5101, 5513, 5725, 6161, 7813, 8321, 9113, 9385, 10805, 11101, 12013, 12961, 13613, 14621, 15665, 16021

Offset: 0

Author

Wolfdieter Lang, Feb 24 2005

Keywords

• nonn
• easy

Comments

It is clear that the a(n) are natural numbers since only odd primes appear in the formula below.

Formula

a(n)=A103728(n+2, 2)=(1 + (p(n+2)-1)*binomial(p(n+2)-1, 2))/p(n+2), with p(n):=A000040(n) (n-th prime).

a(n)= (5 - 4*p(n+2) + p(n+2)^2)/2 = sum(A103718(k, m)*p(n+2)^m, m=0..2)/2.