OFFSET
0,3
COMMENTS
a(n) is sum of all numbers k for which A001414(k), the sum of prime factors with repetition, equals n. See Havermann's link. - J. M. Bergot, Jun 14 2013
REFERENCES
S.M. Kerawala, On a Pair of Arithmetic Functions Analogous to Chawla's Pair, J. Natural Sciences and Mathematics, 9 (1969), circa p. 103.
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
Seiichi Manyama, Table of n, a(n) for n = 0..6274 (terms 0..500 from T. D. Noe)
MAPLE
b:= proc(n, i) option remember;
if n<0 then 0
elif n=0 then 1
elif i=0 then 0
else b(n, i-1) +b(n-ithprime(i), i) *ithprime(i)
fi
end:
a:= n-> b(n, numtheory[pi](n)):
seq(a(n), n=0..40); # Alois P. Heinz, Nov 20 2010
MATHEMATICA
b[n_, i_] := b[n, i] = Which[n<0, 0, n==0, 1, i==0, 0, True, b[n, i-1] + b[n - Prime[i], i]*Prime[i]]; a[n_] := b[n, PrimePi[n]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *)
With[{nn=40}, CoefficientList[Series[1/Product[1-Prime[k]x^Prime[k], {k, nn}], {x, 0, nn}], x]] (* Harvey P. Dale, Jun 20 2021 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(1/prod(k=1, N, 1-isprime(k)*k*x^k)) \\ Seiichi Manyama, Feb 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Better description and more terms from Vladeta Jovovic, May 09 2003
STATUS
approved