A103730 Negative of column k=3 sequence of array A103728.

3, 17, 109, 203, 527, 773, 1473, 3163, 3929, 6947, 9639, 11213, 14857, 21683, 30333, 33659, 45077, 53969, 58823, 75113, 87493, 108503, 141407, 160099, 170033, 191117, 202283, 225903, 322937, 355029, 407047, 425453, 525843, 547649, 616667, 691253

Offset: 0

Author

Wolfdieter Lang, Feb 24 2005

Keywords

• nonn
• easy

Comments

The two a(n) formulas, given below, produce natural numbers for all n>=0.

Formula

a(n)=-A103728(n+3, 3)=-(1 -(p(n+3)-1)*binomial(p(n+3)-1, 3))/p(n+3), with p(n):=A000040(n) (n-th prime).

a(n)= -(17 - 17*p(n+3) + 7*p(n+3)^2 - p(n+3)^3)/3! = -sum(A103718(k, m)*p(n+3)^m, m=0..3)/3!.