A338541 Numbers having exactly four non-unitary prime factors.

44100, 88200, 108900, 132300, 152100, 176400, 213444, 217800, 220500, 260100, 264600, 298116, 304200, 308700, 324900, 326700, 352800, 396900, 426888, 435600, 441000, 456300, 476100, 485100, 509796, 520200, 529200, 544500, 573300, 592900, 596232, 608400, 617400

Offset: 1

Author

Amiram Eldar, Nov 01 2020

Keywords

• nonn

Comments

Numbers k such that A056170(k) = A001221(A057521(k)) = 4.

Numbers divisible by the squares of exactly four distinct primes.

The asymptotic density of this sequence is (eta_1^4 - 6*eta_1^2*eta_2 + 3*eta_2^2 + 8*eta_1*eta_3 - 6*eta_4)/(4*Pi^2) = 0.0000970457..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).

Examples

			44100 = 2^2 * 3^2 * 5^2 * 7^2 is a term since it has exactly 4 prime factors, 2, 3, 5 and 7, that are non-unitary.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Carl Pomerance and Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2011), pp. 52-66. See pp. 61-62.

Crossrefs

Subsequence of A013929 and A318720.

Cf. A001221, A056170, A057521, A190641, A338539, A338540, A338542.

Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324835 (eta_4).

Programs

Mathematica

Select[Range[620000], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 4 &]