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

1,1

Comments

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

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.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A006567, A014614, A097393, A109018, A109023, A109024, A109026, A109027, A109028, A109029, A109030, A109031.

Sequence in context: A206088 A029770 A028529 * A028535 A108094 A162007

Adjacent sequences: A109022 A109023 A109024 * A109026 A109027 A109028

Keyword

nonn,base

Author

Jonathan Vos Post, Jun 16 2005

Extensions

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

Status

approved