A247396 Number of even numbers in classes of classification of the positive numbers defined in comment in A247395.

0, 1, 3, 8, 12, 36, 24, 60, 36, 84, 156, 60, 204, 156, 84, 180, 300, 336, 120, 384, 276, 144, 456, 324, 516, 744, 396, 204, 420, 216, 444, 1680, 516, 804, 276, 1440, 300, 924, 960, 660, 1020, 1056, 360, 1860, 384, 780, 396, 2460, 2604, 900, 456, 924, 1416, 480

Offset: 0

Author

Vladimir Shevelev, Sep 16 2014

Keywords

• nonn

Comments

In the classification every class contains no more than a finite number of numbers with a given least prime divisor.

Examples

			a(6) = (prime(6)^2 - prime(5)^2)/2 = (13^2 - 11^2)/2 = 24. - _Indranil Ghosh_, Mar 08 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..1000
• Vladimir Shevelev, A classification of the positive integers over primes

Crossrefs

Cf. A000040, A156759, A247393, A247394, A247395.

Programs

Maple

A247396:=n->(ithprime(n)^2 - ithprime(n-1)^2)/2: 0,1,3,seq(A247396(n), n=3..100); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

a[0] = 0; a[1] = 1; a[2] = 3; a[n_] := (Prime[n]^2 - Prime[n - 1]^2) / 2; Table[a[n], {n, 0, 53}] (* Indranil Ghosh, Mar 08 2017 *)

PARI

for(n=0, 53, print1(if(n>2, (prime(n)^2 - prime(n - 1)^2)/2, if(n<2, n, 3)),", ")) \\ Indranil Ghosh, Mar 08 2017

Formula

For n>=3, a(n) = (prime(n)^2 - prime(n-1)^2)/2.

Extensions

More terms from Peter J. C. Moses, Sep 17 2014