A030012 Euler transform of {1, primes}.

1, 3, 6, 14, 27, 58, 109, 216, 402, 760, 1390, 2550, 4569, 8178, 14408, 25280, 43850, 75685, 129436, 220226, 371906, 624840, 1043178, 1733108, 2863422, 4709222, 7706800, 12558213, 20372860, 32917707, 52971756, 84923643, 135640660, 215886778, 342419132

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A008578.

Programs

Maple

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: c:= etr(k-> `if`(k<=1, k, ithprime(k-1))): a:= n-> c(n+1): seq(a(n), n=0..40);  # Alois P. Heinz, Sep 07 2008

Mathematica

etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; b]; c = etr[If[# <= 1, #, Prime[#-1]]&]; a = c[#+1]&; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)