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A338542
Numbers having exactly five non-unitary prime factors.
4
5336100, 7452900, 10672200, 12744900, 14905800, 15920100, 16008300, 18404100, 21344400, 22358700, 23328900, 25489800, 26680500, 29811600, 31472100, 31840200, 32016600, 36072036, 36808200, 37088100, 37264500, 37352700, 38234700, 39312900, 42380100, 42688800, 43956900
OFFSET
1,1
COMMENTS
Numbers k such that A056170(k) = A001221(A057521(k)) = 5.
Numbers divisible by the squares of exactly five distinct primes.
The asymptotic density of this sequence is (eta_1^5 - 10*eta_1^3*eta_2 + 15*eta_1*eta_2^2 + 20*eta_1^2*eta_3 - 20*eta_2*eta_3 - 30*eta_1*eta_4 + 24*eta_5)/(20*Pi^2) = 0.0000015673..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).
LINKS
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
5336100 = 2^2 * 3^2 * 5^2 * 7^2 * 11^2 is a term since it has exactly 5 prime factors, 2, 3, 5, 7 and 11, that are non-unitary.
MATHEMATICA
Select[Range[2*10^7], Count[FactorInteger[#][[;; , 2]], _?(#1 > 1 &)] == 5 &]
CROSSREFS
Subsequence of A013929, A318720 and A327877.
Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324835 (eta_4), A324836 (eta_5).
Sequence in context: A303791 A058252 A147528 * A115960 A186014 A234496
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2020
STATUS
approved