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

1,1

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).

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.

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A260104 A031789 A001294 * A217183 A034415 A201510

Adjacent sequences: A109023 A109024 A109025 * A109027 A109028 A109029

Keyword

nonn,base

Author

Jonathan Vos Post, Jun 16 2005

Status

approved