A143346 The number of distinct prime factors occurring in the numbers between n^2 and (n+1)^2.

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

Offset

1,1

Comments

Same as the number of distinct prime factors in (2n^2+2n)!/(n^2)!. The plot appears nearly linear.

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Example

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.

Mathematica

Table[a=n^2; b=a+2*n; Sum[Sign[Quotient[b, p]-Quotient[a, p]], {p, Prime[Range[PrimePi[b]]]}], {n, 100}]

Crossrefs

Cf. A014085 (number of primes between n^2 and (n+1)^2).

Sequence in context: A225773 A233671 A348854 * A189010 A189221 A189170

Adjacent sequences: A143343 A143344 A143345 * A143347 A143348 A143349

Keyword

nonn

Author

T. D. Noe, Aug 09 2008

Status

approved