A128302 The indices of cubes (of primes) in the 3-almost primes.

1, 5, 30, 82, 328, 551, 1243, 1763, 3112, 6276, 7619, 12972, 17615, 20322, 26514, 37977, 52220, 57703, 76200, 90701, 98470, 124541, 144229, 177395, 229275, 258410, 273908, 306750, 324149, 360724, 510225, 559384, 638657, 666743, 819645, 852588

Offset: 1

Author

Rick L. Shepherd, Feb 25 2007

Keywords

• nonn

Comments

the primepi function might be used to find terms. But it is expensive for larger numbers so then one might use A335331 to ease finding primepi(m) for larger m. - David A. Corneth, Apr 13 2025

Examples

			a(4) = 82 as 343 = 7^3 = prime(4)^3, the fourth cube in the 3-almost primes, is the eighty-second 3-almost prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..590
• David A. Corneth, PARI program

Crossrefs

Cf. A000040, A014612, A030078, A128301, A128303, A335331.

Programs

Mathematica

Position[Select[Range[10^6], PrimeOmega[#] == 3 &], ?(PrimeNu[#] == 1 &)] // Flatten (* _Amiram Eldar, Apr 13 2025 *)

PARI

list(lim) = {my(f, c); for(k = 1, lim, f = factor(k); if(bigomega(f) == 3, c++; if(omega(f) == 1, print1(c, ", "))));} \\ Amiram Eldar, Apr 13 2025

PARI

\\ See Corneth link

Formula

A014612(a(n)) = A030078(n) = A000040(n)^3.