cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A338542 Numbers having exactly five non-unitary prime factors.

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%I A338542 #10 Nov 02 2020 02:00:16
%S A338542 5336100,7452900,10672200,12744900,14905800,15920100,16008300,
%T A338542 18404100,21344400,22358700,23328900,25489800,26680500,29811600,
%U A338542 31472100,31840200,32016600,36072036,36808200,37088100,37264500,37352700,38234700,39312900,42380100,42688800,43956900
%N A338542 Numbers having exactly five non-unitary prime factors.
%C A338542 Numbers k such that A056170(k) = A001221(A057521(k)) = 5.
%C A338542 Numbers divisible by the squares of exactly five distinct primes.
%C A338542 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).
%H A338542 Amiram Eldar, <a href="/A338542/b338542.txt">Table of n, a(n) for n = 1..10000</a>
%H A338542 Carl Pomerance and Andrzej Schinzel, <a href="http://mjcnt.phystech.edu/en/article.php?id=4">Multiplicative Properties of Sets of Residues</a>, Moscow Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2011), pp. 52-66. See pp. 61-62.
%e A338542 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.
%t A338542 Select[Range[2*10^7], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 5 &]
%Y A338542 Subsequence of A013929, A318720 and A327877.
%Y A338542 Cf. A001221, A056170, A057521, A190641, A338539, A338540, A338541.
%Y A338542 Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324835 (eta_4), A324836 (eta_5).
%K A338542 nonn
%O A338542 1,1
%A A338542 _Amiram Eldar_, Nov 01 2020