OFFSET
1,2
COMMENTS
Apply "INVERT" transform to primes.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 200 terms from T. D. Noe)
N. J. A. Sloane, Transforms
FORMULA
INVERT: a's from b's in 1+Sum a_i x^i = 1/(1-Sum b_i x^i).
G.f: (1-b(x)/(b(x)-1))*x, where b(x) is the g.f. of A000040. - Mario C. Enriquez, Dec 13 2016
EXAMPLE
a(5) = 25*2 +7*3 +2*5 + 1*7 = 88.
MAPLE
a:= proc(n) option remember; `if`(n=1, 1,
add(a(n-i)*ithprime(i), i=1..n-1))
end:
seq(a(n), n=1..29); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
CoefficientList[ Series[ 1/(1 - Sum[ Prime[ n ]*x^n, {n, 1, 25} ] ), {x, 0, 25} ], x ]
(* Second program: *)
a[1] = 1; a[m_] := a[m] = Sum[Prime@ k a[m - k], {k, m - 1}]; Table[a@ n, {n, 25}] (* Michael De Vlieger, Dec 13 2016 *)
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
STATUS
approved