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A109025 Numbers that have exactly five prime factors counted with multiplicity (A014614) whose digit reversal is different and also has 5 prime factors (with multiplicity).

%I A109025 #28 Feb 16 2025 08:32:58
%S A109025 270,1386,1575,2070,2136,2142,2295,2300,2394,2412,2475,2508,2550,2565,
%T A109025 2568,2610,2844,2964,3087,3267,3465,3654,3708,3924,4008,4016,4068,
%U A109025 4185,4208,4290,4293,4347,4446,4482,4563,4692,4779,4875,4932,5049,5238,5355
%N A109025 Numbers that have exactly five prime factors counted with multiplicity (A014614) whose digit reversal is different and also has 5 prime factors (with multiplicity).
%C A109025 This sequence is the k = 5 instance of the series which begins with k = 1, k = 2, k = 3 (A109023), k = 4 (A109024).
%H A109025 David A. Corneth, <a href="/A109025/b109025.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)
%H A109025 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A109025 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Emirp.html">Emirp</a>.
%H A109025 Eric Weisstein and Jonathan Vos Post, <a href="https://mathworld.wolfram.com/Emirpimes.html">Emirpimes</a>.
%e A109025 a(2) = 1386 is in this sequence because 1386 = 2 * 3^2 * 7 * 11 has exactly 5 prime factors counted with multiplicity and reverse(1386) = 6831 = 3^3 * 11 * 23 is also has exactly 5 prime factors counted with multiplicity.
%e A109025 5355 is in this sequence because 5355 = 3^2 * 5 * 7 * 17 and reverse(5355) = 5535 = 3^3 * 5 * 41.
%t A109025 Select[Range[6000],!PalindromeQ[#]&&Total[FactorInteger[#][[All,2]]]==Total[ FactorInteger[ IntegerReverse[#]][[All,2]]]==5&] (* _Harvey P. Dale_, Nov 20 2022 *)
%o A109025 (PARI) is(n) = {
%o A109025 	my(r = fromdigits(Vecrev(digits(n))));
%o A109025 	n!=r && bigomega(n) == 5 && bigomega(r) == 5
%o A109025 } \\ _David A. Corneth_, Mar 07 2024
%Y A109025 Cf. A006567, A014614, A097393, A109018, A109023, A109024, A109026, A109027, A109028, A109029, A109030, A109031.
%K A109025 nonn,base
%O A109025 1,1
%A A109025 _Jonathan Vos Post_, Jun 16 2005
%E A109025 Typo in definition corrected by _Harvey P. Dale_, Nov 20 2022