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

0,3

Comments

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

Links

Indranil Ghosh, Table of n, a(n) for n = 0..1000

Vladimir Shevelev, A classification of the positive integers over primes

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A032217 A032142 A032046 * A180507 A218889 A131213

Adjacent sequences: A247393 A247394 A247395 * A247397 A247398 A247399

Keyword

nonn,changed

Author

Vladimir Shevelev, Sep 16 2014

Extensions

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

Status

approved