A228578 Sum of the distinct prime factors of the squarefree semiprimes (A006881).

5, 7, 9, 8, 10, 13, 15, 14, 19, 12, 21, 16, 25, 20, 16, 22, 31, 33, 18, 26, 39, 18, 43, 22, 45, 32, 20, 34, 49, 24, 55, 40, 28, 61, 24, 63, 44, 46, 26, 69, 50, 73, 24, 34, 75, 36, 81, 56, 30, 85, 62, 91, 64, 42, 28, 99, 70, 103, 36, 46, 105, 30, 74, 109, 48, 38, 111

Offset

1,1

Comments

Sum of the distinct prime factors of A006881(n). If A006881(n) is even then a(n) = A006881(n)/2 + 2. If A006881(n) is odd then a(n) is even.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = sopf(A006881(n)) = A008472(A006881(n)).

Also, a(n) = sopfr(A006881(n)) = A001414(A006881(n)) because A006881 are squarefree. - Zak Seidov, Oct 28 2015

Example

a(1) = 5, since 6 is the first squarefree semiprime and the sum of the distinct prime factors of 6 is 2 + 3 = 5. a(2) = 7 since 10 is the second squarefree semiprime and the sum of the distinct prime factors of 10 is 2 + 5 = 5.

Mathematica

Total[First /@ FactorInteger@ #] & /@ Select[Range@ 240, PrimeNu@ # == 2 && SquareFreeQ@ # &] (* Michael De Vlieger, Oct 28 2015 *)

Prog

(PARI) do(x)=my(v=List()); forprime(p=3, x\2, forprime(q=2, min(x\p, p-1), listput(v, [p*q, p+q]))); v=vecsort(Vec(v), 1); apply(u->u[2], v) \\ Charles R Greathouse IV, Nov 05 2017

Crossrefs

Cf. A006881, A001414, A008472.

Sequence in context: A135913 A308713 A109352 * A242742 A323602 A164029

Adjacent sequences: A228575 A228576 A228577 * A228579 A228580 A228581

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Aug 28 2013

Extensions

a(61)-a(67) corrected by Michael De Vlieger, Oct 28 2015

Status

approved