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

1,1

Links

Table of n, a(n) for n=1..37.

Formula

Intersection of A002113 and A051270.

Example

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.

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 *)

Prog

(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}

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).

Sequence in context: A250514 A343432 A115429 * A046395 A143043 A031605

Adjacent sequences: A373462 A373463 A373464 * A373466 A373467 A373468

Keyword

nonn,base,changed

Author

M. F. Hasler, Jun 06 2024

Status

approved