A373465 Palindromes with exactly 5 distinct prime divisors.

6006, 8778, 20202, 28182, 40404, 41514, 43134, 50505, 60606, 63336, 66066, 68586, 80808, 83538, 86268, 87978, 111111, 141141, 168861, 171171, 202202, 204402, 209902, 210012, 212212, 219912, 225522, 231132, 232232, 239932, 246642, 249942, 252252, 258852, 262262, 266662, 272272

Offset: 1

Author

M. F. Hasler, Jun 06 2024

Keywords

• nonn
• base

Examples

			a(1) = 6006 = 2 * 3 * 7 * 11 * 13 is a palindrome (A002113) with 5 prime divisors.
a(5) = 40404 = 2^2 * 3 * 7 * 13 * 37 also is a palindrome with 5 prime divisors, although the divisor 2 occurs twice as a factor in the factorization.
		

Crossrefs

Cf. A002113 (palindromes), A051270 (omega(.) = 5).

Cf. A046331 (same but counting prime factors with multiplicity), A046395 (same but squarefree), A373466 (same with omega = 6), A373467 (with omega = 7).

Programs

Mathematica

Select[Range[300000],PalindromeQ[#]&&Length[FactorInteger[#]]==5&] (* James C. McMahon, Jun 08 2024 *)
Select[Range[300000],PalindromeQ[#]&&PrimeNu[#]==5&] (* Harvey P. Dale, Sep 01 2024 *)

PARI

A373465_upto(N, start=1, num_fact=5)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && listput(L, start)); L}

Formula

Intersection of A002113 and A051270.