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A109027 Numbers that have exactly seven prime factors counted with multiplicity (A046308) whose digit reversal is different and also has 7 prime factors (with multiplicity).

%I A109027 #24 Feb 16 2025 08:32:58
%S A109027 8820,21240,21708,21780,21920,23280,23472,23625,23800,25560,25584,
%T A109027 25758,26280,27432,27504,27888,27900,28836,29250,29403,29736,29970,
%U A109027 30492,34884,36828,40338,40572,40950,41976,42228,42984,43659,43956,44128
%N A109027 Numbers that have exactly seven prime factors counted with multiplicity (A046308) whose digit reversal is different and also has 7 prime factors (with multiplicity).
%C A109027 This sequence is the k = 7 instance of the series which begins with k = 1 (emirps), k = 2, k = 3, k = 4, k = 5 (A109025), k = 6 (A109026).
%H A109027 David A. Corneth, <a href="/A109027/b109027.txt">Table of n, a(n) for n = 1..10000</a>
%H A109027 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A109027 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Emirp.html">Emirp</a>.
%H A109027 Eric Weisstein and Jonathan Vos Post, <a href="https://mathworld.wolfram.com/Emirpimes.html">Emirpimes</a>.
%e A109027 a(20) = 29403 is in this sequence because 29403 = 3^5 * 11^2 has exactly 7 prime factors counted with multiplicity and reverse(29403) = 30492 = 2^2 * 3^2 * 7 * 11^2 also has exactly 7 prime factors counted with multiplicity.
%t A109027 Select[Range[45000],!PalindromeQ[#]&&PrimeOmega[#]==PrimeOmega[ IntegerReverse[ #]] ==7&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 02 2019 *)
%o A109027 (PARI) is(n) = {
%o A109027 	my(r = fromdigits(Vecrev(digits(n))));
%o A109027 	n!=r && bigomega(n) == 7 && bigomega(r) == 7
%o A109027 } \\ _David A. Corneth_, Mar 07 2024
%Y A109027 Cf. A046308, A006567, A097393, A109018, A109023, A109024, A109025, A109026, A109028, A109029, A109030, A109031.
%K A109027 nonn,base
%O A109027 1,1
%A A109027 _Jonathan Vos Post_, Jun 16 2005