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A109026 Numbers that have exactly six prime factors counted with multiplicity (A046306) whose digit reversal is different and also has 6 prime factors (with multiplicity).

%I A109026 #28 Mar 11 2025 14:07:37
%S A109026 2576,2970,4284,4356,4410,4600,4698,4824,5265,5625,6534,6752,6900,
%T A109026 8250,8964,10710,10890,13140,13986,16236,16335,17577,18504,19494,
%U A109026 20286,20574,21114,21150,21160,21336,21492,21576,21609,21900,21996,22392,22770
%N A109026 Numbers that have exactly six prime factors counted with multiplicity (A046306) whose digit reversal is different and also has 6 prime factors (with multiplicity).
%C A109026 This sequence is the k = 6 instance of the series which begins with k = 1, k = 2, k = 3 (A109023), k = 4 (A109024), k = 5 (A109025).
%H A109026 David A. Corneth, <a href="/A109026/b109026.txt">Table of n, a(n) for n = 1..10000</a> (first 3500 terms from Harvey P. Dale)
%H A109026 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A109026 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Emirp.html">Emirp</a>.
%H A109026 Eric Weisstein and Jonathan Vos Post, <a href="https://mathworld.wolfram.com/Emirpimes.html">Emirpimes</a>.
%e A109026 a(1) = 2576 is in this sequence because 2576 = 2^4 * 7 * 23 has exactly 6 prime factors counted with multiplicity reverse(2576) = 6752 = 2^5 * 211 is also has exactly 6 prime factors counted with multiplicity.
%t A109026 Select[Range[23000],!PalindromeQ[#]&&Total[FactorInteger[#][[All,2]]] == Total[FactorInteger[IntegerReverse[#]][[All,2]]]==6&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 10 2017 *)
%t A109026 Select[Range[25000],PrimeOmega[#]==PrimeOmega[IntegerReverse[#]]==6&&!PalindromeQ[#]&] (* _Harvey P. Dale_, Mar 11 2025 *)
%o A109026 (PARI) is(n) = {
%o A109026 	my(r = fromdigits(Vecrev(digits(n))));
%o A109026 	n!=r && bigomega(n) == 6 && bigomega(r) == 6
%o A109026 } \\ _David A. Corneth_, Mar 07 2024
%Y A109026 Cf. A046306, A006567, A097393, A109018, A109023, A109024, A109025, A109027, A109028, A109029, A109030, A109031.
%K A109026 nonn,base
%O A109026 1,1
%A A109026 _Jonathan Vos Post_, Jun 16 2005