A128304 Indices of 4th powers (of primes) in the 4-almost primes.

1, 8, 90, 385, 2556, 5138, 15590, 24646, 53993, 139199, 182476, 375363, 569617, 691012, 991150, 1613115, 2490040, 2849478, 4163793, 5263838, 5888203, 8100907, 9886861, 13102875, 18538021, 21816421, 23608907, 27525519, 29659283, 34290671

Offset: 1

Author

Rick L. Shepherd, Mar 05 2007

Keywords

• nonn

Examples

			a(3) = 90 as 625 = 5^4 = prime(3)^4, the third 4th power in the 4-almost primes, is the 90th 4-almost prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..99 (terms 1..40 from Zak Seidov)

Crossrefs

Cf. A000040, A014613, A030514, A128303, A128305.

Programs

Mathematica

Position[Select[Range[10^6], PrimeOmega[#] == 4 &], ?(PrimeNu[#] == 1 &)] // 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(omega(f) == 1, print1(c, ", "))));} \\ Amiram Eldar, Apr 13 2025

Formula

A014613(a(n)) = A030514(n) = A000040(n)^4.