A109025 Numbers that have exactly five prime factors counted with multiplicity (A014614) whose digit reversal is different and also has 5 prime factors (with multiplicity).

270, 1386, 1575, 2070, 2136, 2142, 2295, 2300, 2394, 2412, 2475, 2508, 2550, 2565, 2568, 2610, 2844, 2964, 3087, 3267, 3465, 3654, 3708, 3924, 4008, 4016, 4068, 4185, 4208, 4290, 4293, 4347, 4446, 4482, 4563, 4692, 4779, 4875, 4932, 5049, 5238, 5355

Offset: 1

Author

Jonathan Vos Post, Jun 16 2005

Keywords

• nonn
• base

Comments

This sequence is the k = 5 instance of the series which begins with k = 1, k = 2, k = 3 (A109023), k = 4 (A109024).

Examples

			a(2) = 1386 is in this sequence because 1386 = 2 * 3^2 * 7 * 11 has exactly 5 prime factors counted with multiplicity and reverse(1386) = 6831 = 3^3 * 11 * 23 is also has exactly 5 prime factors counted with multiplicity.
5355 is in this sequence because 5355 = 3^2 * 5 * 7 * 17 and reverse(5355) = 5535 = 3^3 * 5 * 41.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 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. A006567, A014614, A097393, A109018, A109023, A109024, A109026, A109027, A109028, A109029, A109030, A109031.

Programs

Mathematica

Select[Range[6000],!PalindromeQ[#]&&Total[FactorInteger[#][[All,2]]]==Total[ FactorInteger[ IntegerReverse[#]][[All,2]]]==5&] (* Harvey P. Dale, Nov 20 2022 *)

PARI

is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 5 && bigomega(r) == 5
} \\ David A. Corneth, Mar 07 2024

Extensions

Typo in definition corrected by Harvey P. Dale, Nov 20 2022