A128303 Indices of squares (of semiprimes) in the 4-almost primes.

1, 3, 8, 12, 24, 29, 59, 66, 90, 97, 162, 172, 187, 224, 234, 335, 385, 412, 489, 531, 551, 630, 692, 791, 921, 997, 1128, 1223, 1256, 1285, 1420, 1484, 1518, 1549, 1937, 2146, 2315, 2441, 2483, 2556, 2606, 2651, 2915, 3124, 3175, 3542, 3587, 3645, 3751, 3800

Offset: 1

Author

Rick L. Shepherd, Mar 04 2007

Keywords

• nonn

Examples

			a(5) = 24 as 196 = 14^2 = semiprime(5)^2, the 5th square in the 4-almost primes, is the 24th 4-almost prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014613, A074985, A001358, A128302, A128304.

Programs

Mathematica

Position[Select[Range[3*10^4], PrimeOmega[#] == 4 &], ?(IntegerQ[Sqrt[#]] &)] // Flatten (* _Amiram Eldar, Apr 13 2025 *)

PARI

list(lim) = {my(f, c); for(k = 1, lim, f = factor(k); if(bigomega(f) == 4, c++; if(vecprod(f[,2]) == 4, print1(c, ", "))));} \\ Amiram Eldar, Apr 13 2025

Formula

A014613(a(n)) = A074985(n) = A001358(n)^2.