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A123567
Recursive sum of 2*Omega(n), where Omega(n) is the sequence A001222.
1
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
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
KEYWORD
nonn
AUTHOR
Carlos Alves, Nov 12 2006
STATUS
approved