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A226068
The sum of the positive integers not exceeding 2n that are representable as the sum of two successive sexy primes.
2
0, 0, 0, 0, 0, 0, 0, 16, 16, 36, 36, 36, 36, 64, 64, 96, 96, 96, 96, 136, 136, 136, 136, 136, 136, 188, 188, 188, 188, 188, 188, 188, 188, 256, 256, 256, 256, 256, 256, 336, 336, 336, 336, 424, 424, 424, 424, 424
OFFSET
1,8
COMMENTS
4 divides a(n) for n > 0.
FORMULA
a(n) = 2*Sum_{i=1..n} i * (pi(i-3) - pi(i-4)) * (pi(i+3) - pi(i+2)), where pi is the prime counting function (A000720).
a(n) = Sum_{i=1..2*n} c(i), where c is the characteristic function of A104010. - R. J. Mathar, May 28 2013
MAPLE
with(numtheory); A226068:=n->sum( 2*i*(pi(i-3) - pi(i-4)) * (pi(i+3) - pi(i+2)) , i = 1..n);
seq(A226068(k), k = 1..70);
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 24 2013
STATUS
approved