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A082767
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Number of edges in the prime graph.
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0
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1, 3, 5, 7, 9, 12, 14, 16, 18, 21, 23, 26, 28, 31, 34, 36, 38, 41, 43, 46, 49, 52, 54, 57, 59, 62, 64, 67, 69, 73, 75, 77, 80, 83, 86, 89, 91, 94, 97, 100, 102, 106, 108, 111, 114, 117, 119, 122
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The prime graph is defined to be the graph formed by writing the integers 0 to n in a straight line as vertices and then connecting i and j (i>j) iff i-j=1 or i=j+p, where p is a prime factor of i. It can be visualized as the Sieve of Eratosthenes, with each integer connected to its neighbors and the striking out process as a wave forming the remaining edges. omega(n) is the number of distinct prime factors of n.
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FORMULA
| a(n) = a(n-1) + 1 + omega(n)
a(n) = sum INT[n/p], p is 1 or a prime, p < or = n. a(12) = [12/1] + [12/2] + [12/3] + [12/5] + [12/7] + [12/11] = 12+6+4+2+1+1 = 26. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 06 2005
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EXAMPLE
| a(1)=1. a(2)=a(1)+1+omega(2)=1+1+1=3. a(6)=a(5)+1+omega(6)=9+1+2=12.
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PROG
| (PARI) a=1; c=2; while (c<50, print1(a", "); a=a+1+omega(c); c++)
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CROSSREFS
| Sequence in context: A190328 A033036 A198082 * A047932 A139130 A186705
Adjacent sequences: A082764 A082765 A082766 * A082768 A082769 A082770
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KEYWORD
| nonn
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), May 24 2003
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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