A002125 a(n) = Sum_{k=0..n} f(k)*f(n-k) where f(k) = A002124(k).
1, 0, 0, 2, 0, 2, 3, 2, 6, 4, 9, 14, 11, 26, 29, 34, 62, 68, 99, 140, 169, 252, 322, 430, 607, 764, 1059, 1424, 1845, 2546, 3344, 4442, 6002, 7876, 10575, 14058, 18575, 24878, 32842, 43630, 58073, 76658, 101913, 134964, 178468, 236776, 312874, 414094, 547947, 723646
Offset: 0
Keywords
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- N. J. A. Sloane, Table of n, a(n) for n = 0..1000
- P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. = Coll. Papers, II, pp. 354-380. [The sequence I_n]
Programs
-
Haskell
a002125 n = a002125_list !! n a002125_list = uncurry conv $ splitAt 1 a002124_list where conv xs (z:zs) = sum (zipWith (*) xs $ reverse xs) : conv (z:xs) zs -- Reinhard Zumkeller, Mar 21 2014
-
Maple
M:=120; f:=array(0..M); f[0]:=1; f[1]:=0; f[2]:=0; for n from 3 to M do t1:=0; for k from 2 to n do p := ithprime(k); if p <= n then t1 := t1 + f[n-p]; fi; od: f[n]:=t1; od: # f is A002124 A002125:=array(0..M); for n from 0 to M do A002125[n]:=add(f[t]*f[n-t],t=0..n); od: [seq(A002125[n],n=0..M)];
-
Mathematica
CoefficientList[Series[1/(1 - Sum[x^Prime[k], {k, 2, 50}])^2, {x, 0, 50}], x] (* Indranil Ghosh, Apr 12 2017 *)
Formula
G.f.: 1/(1 - Sum_{k>=2} x^prime(k))^2. - Ilya Gutkovskiy, Apr 11 2017
Extensions
Edited by N. J. A. Sloane, Dec 03 2006
Comments