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Search: id:A143346
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| A143346 |
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The number of distinct prime factors occurring in the numbers between n^2 and (n+1)^2. |
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+0
1
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| 2, 4, 6, 8, 9, 12, 13, 14, 17, 18, 20, 22, 23, 26, 25, 29, 30, 32, 33, 36, 37, 37, 41, 42, 44, 45, 45, 51, 49, 53, 54, 53, 58, 57, 62, 62, 65, 63, 66, 70, 70, 72, 73, 74, 78, 77, 79, 84, 81, 86, 85, 90, 87, 93, 93, 94, 97, 99, 99, 100, 102, 105, 105, 109, 109, 109, 115, 111
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Same as the number of distinct prime factors in (2n^2+2n)!/(n^2)!. The plot appears nearly linear.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
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The numbers between 4 and 9 have factorizations 5, 2*3, 7, 2^4, which use primes 2, 3, 5 and 7. Hence a(2)=4.
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MATHEMATICA
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Table[a=n^2; b=a+2*n; Sum[Sign[Quotient[b, p]-Quotient[a, p]], {p, Prime[Range[PrimePi[b]]]}], {n, 100}]
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CROSSREFS
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Cf. A014085 (number of primes between n^2 and (n+1)^2).
Sequence in context: A114571 A050091 A047294 this_sequence A138969 A071562 A100345
Adjacent sequences: A143343 A143344 A143345 this_sequence A143347 A143348 A143349
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 09 2008
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