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A109029
Numbers that have exactly nine prime factors counted with multiplicity (A046312) whose digit reversal is different and also has 9 prime factors (with multiplicity).
10
21168, 23424, 23616, 27456, 41184, 42432, 48114, 61632, 65472, 86112, 211410, 212256, 213192, 215232, 217440, 219072, 230208, 232512, 236925, 236928, 238656, 238680, 251100, 251505, 251748, 253824, 255024, 255960, 257856, 259968, 270912
OFFSET
1,1
COMMENTS
This sequence is the k = 8 instance of the series which begins with k = 1 (emirps), k = 2, k = 3 (A109023), k = 4 (A109024), k = 5 (A109025), k = 6 (A109026), k = 7 (A109027), k = 8 (A109028).
LINKS
Eric Weisstein's World of Mathematics, Almost Prime.
Eric Weisstein's World of Mathematics, Emirp.
Eric Weisstein and Jonathan Vos Post, Emirpimes.
EXAMPLE
a(1) = 21168 is in this sequence because 21168 = 2^4 * 3^3 * 7^2 has exactly 9 prime factors counted with multiplicity and reverse(21168) = 86112 = 2^5 * 3^2 * 13 * 23 also has exactly 9 prime factors counted with multiplicity.
MATHEMATICA
okQ[n_]:=Module[{idn=IntegerDigits[n], ridn}, ridn=Reverse[idn]; idn!=ridn && PrimeOmega[n]==9&&PrimeOmega[FromDigits[ridn]]==9]; Select[Range[ 271000], okQ] (* Harvey P. Dale, Sep 24 2011 *)
PROG
(PARI) is(n) = {
my(r = fromdigits(Vecrev(digits(n))));
n!=r && bigomega(n) == 9 && bigomega(r) == 9
} \\ David A. Corneth, Mar 07 2024
KEYWORD
nonn,base
AUTHOR
Jonathan Vos Post, Jun 16 2005
STATUS
approved