

A228578


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


7



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, p1), 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



