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

1,1

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).

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.

Example

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.

Mathematica

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

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).

Sequence in context: A378097 A359127 A223457 * A190377 A049205 A234426

Adjacent sequences: A338538 A338539 A338540 * A338542 A338543 A338544

Keyword

nonn

Author

Amiram Eldar, Nov 01 2020

Status

approved