A109026 - OEIS

%I #25 Mar 09 2024 11:15:48

%S 2576,2970,4284,4356,4410,4600,4698,4824,5265,5625,6534,6752,6900,

%T 8250,8964,10710,10890,13140,13986,16236,16335,17577,18504,19494,

%U 20286,20574,21114,21150,21160,21336,21492,21576,21609,21900,21996,22392,22770

%N 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 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Emirp.html">Emirp</a>.

%H Eric Weisstein and Jonathan Vos Post, <a href="http://mathworld.wolfram.com/Emirpimes.html">Emirpimes</a>.

%e 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 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 *)

%o (PARI) is(n) = {

%o 	my(r = fromdigits(Vecrev(digits(n))));

%o 	n!=r && bigomega(n) == 6 && bigomega(r) == 6

%o } \\ _David A. Corneth_, Mar 07 2024

%Y Cf. A046306, A006567, A097393, A109018, A109023, A109024, A109025, A109027, A109028, A109029, A109030, A109031.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Jun 16 2005