A123567 Recursive sum of 2*Omega(n), where Omega(n) is the sequence A001222.

3, 5, 7, 11, 13, 17, 19, 25, 29, 33, 35, 41, 43, 47, 51, 59, 61, 67, 69, 75, 79, 83, 85, 93, 97, 101, 107, 113, 115, 121, 123, 133, 137, 141, 145, 153, 155, 159, 163, 171, 173, 179, 181, 187, 193, 197, 199, 209, 213, 219, 223, 229, 231, 239, 243, 251, 255, 259, 261

Offset

1,1

Comments

Note that the first 7 terms are prime numbers. See also the sum of Omega (A022559).

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n+1) = a(n) + 2*A001222(n), with a(1)=3.

Example

a(2)=a(1)+2*Omega(1)=3+2=5;
a(3)=a(2)+2*Omega(2)=5+2=7;
a(4)=a(3)+2*Omega(3)=7+4=11;

Mathematica

Omega = Plus @@ Sum[Transpose[FactorInteger[ # ]][[2]]] &; FoldList[Plus, 3, 2Map[Omega, Range[2, 200]]]
nxt[{n_, a_}]:={n+1, a+2PrimeOmega[n]}; Rest[Transpose[NestList[nxt, {1, 3}, 60]][[2]]] (* Harvey P. Dale, Mar 13 2016 *)
Fold[Append[#1, Last[#1] + 2 PrimeOmega[#2]] &, {3}, Range[2, 59]] (* Michael De Vlieger, Oct 16 2017 *)

Crossrefs

Sequence in context: A100276 A225669 A065389 * A059645 A090190 A325143

Adjacent sequences: A123564 A123565 A123566 * A123568 A123569 A123570

Keyword

nonn

Author

Carlos Alves, Nov 12 2006

Status

approved