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A156780
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sp(n)*pi(n) = A034387(n)*A000720(n) = (sum of primes <= n)*(number of primes <= n).
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1
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0, 0, 2, 10, 10, 30, 30, 68, 68, 68, 68, 140, 140, 246, 246, 246, 246, 406, 406, 616, 616, 616, 616, 900, 900, 900, 900, 900, 900, 1290, 1290, 1760, 1760, 1760, 1760, 1760, 1760, 2364, 2364, 2364, 2364, 3094, 3094, 3934, 3934, 3934, 3934, 4920, 4920, 4920
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| All terms are even, since the parity of sp(n)=A034387(n) is always the opposite of pi(n)=A000720(n). Indeed, both change by an odd amount at each prime, starting with the first nonzero values sp(2)=2 and pi(2)=1. Thus one might also consider the integer sequence a(n)/2 = 0, 0, 1, 5, 5, 15, 15, 34, 34, 34, 34, 70, 70, 123, 123, 123, 123, 203, 203, 308,.... Sequence A156778 lists these values (without duplicates).
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FORMULA
| a(n) = 2*A156778( pi(n)), where pi(n) = A000720(n)= PrimePi(n) = #{primes <= n}.
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PROG
| (PARI) vector(80, n, sum(i=1, primepi(n), prime(i))*primepi(n))
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CROSSREFS
| Sequence in context: A156556 A071808 A168381 * A067046 A066394 A033466
Adjacent sequences: A156777 A156778 A156779 * A156781 A156782 A156783
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KEYWORD
| nonn
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AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), Feb 21 2009
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