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).

2576, 2970, 4284, 4356, 4410, 4600, 4698, 4824, 5265, 5625, 6534, 6752, 6900, 8250, 8964, 10710, 10890, 13140, 13986, 16236, 16335, 17577, 18504, 19494, 20286, 20574, 21114, 21150, 21160, 21336, 21492, 21576, 21609, 21900, 21996, 22392, 22770

Offset: 1

Author

Jonathan Vos Post, Jun 16 2005

Keywords

• nonn
• base

Comments

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).

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3500 terms from Harvey P. Dale)
• Eric Weisstein's World of Mathematics, Almost Prime.
• Eric Weisstein's World of Mathematics, Emirp.
• Eric Weisstein and Jonathan Vos Post, Emirpimes.

Crossrefs

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

Programs

Mathematica

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 *)
Select[Range[25000],PrimeOmega[#]==PrimeOmega[IntegerReverse[#]]==6&&!PalindromeQ[#]&] (* Harvey P. Dale, Mar 11 2025 *)

PARI

is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 6 && bigomega(r) == 6
} \\ David A. Corneth, Mar 07 2024