A373465 - OEIS

%I #17 Sep 01 2024 17:41:16

%S 6006,8778,20202,28182,40404,41514,43134,50505,60606,63336,66066,

%T 68586,80808,83538,86268,87978,111111,141141,168861,171171,202202,

%U 204402,209902,210012,212212,219912,225522,231132,232232,239932,246642,249942,252252,258852,262262,266662,272272

%N Palindromes with exactly 5 distinct prime divisors.

%F Intersection of A002113 and A051270.

%e a(1) = 6006 = 2 * 3 * 7 * 11 * 13 is a palindrome (A002113) with 5 prime divisors.

%e 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.

%t Select[Range[300000],PalindromeQ[#]&&Length[FactorInteger[#]]==5&] (* _James C. McMahon_, Jun 08 2024 *)

%t Select[Range[300000],PalindromeQ[#]&&PrimeNu[#]==5&] (* _Harvey P. Dale_, Sep 01 2024 *)

%o (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}

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

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

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jun 06 2024