A046392 -id:A046392 - cp's OEIS frontend

A046399 Smallest squarefree palindrome with exactly n distinct prime factors.

1, 2, 6, 66, 858, 6006, 222222, 22444422, 244868442, 6434774346, 438024420834, 50146955964105, 2415957997595142, 495677121121776594, 22181673755737618122, 5521159517777159511255, 477552751050050157255774

Offset: 0

Patrick De Geest, Jun 15 1998

Initial terms of sequences A046392-A046398.

			a(4) = 858 = 2*3*11*13.

J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), p. 315, Pour la Science, Paris 2000.

Cf. A046385, A076886.

Cf. A046392, A046393, A046394, A046395, A046396, A046397, A046398.

r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[k = 1; While[r[k] != k || !SquareFreeQ[k] || Length[Select[Divisors[k], PrimeQ]] != n, k++ ]; Print[k], {n, 0, 30}] (* Ryan Propper, Sep 16 2005 *)

Edited by N. J. A. Sloane, Dec 06 2008 at the suggestion of R. J. Mathar
a(10)-a(13) from Donovan Johnson, Oct 03 2011
a(14)-a(15) from David A. Corneth, Oct 03 2020
a(15) corrected by Daniel Suteu, Feb 05 2023
a(16) from Michael S. Branicky, Feb 08 2023

A075799 Palindromic numbers which are products of an even number of distinct primes.

Original entry on oeis.org

1, 6, 22, 33, 55, 77, 111, 141, 161, 202, 262, 303, 323, 393, 454, 505, 515, 535, 545, 565, 626, 707, 717, 737, 767, 818, 838, 858, 878, 898, 939, 949, 959, 979, 989, 1111, 1441, 1661, 1991, 2002, 2442, 3003, 3113, 3223, 3443, 3883, 4774, 5005, 5115, 6666, 7117, 7447

Offset: 1

Jani Melik, Oct 13 2002

			1, 111=3*37 and 858=2*3*11*13 are palindromic and products of an even number of distinct primes.

Paolo Xausa, Table of n, a(n) for n = 1..1000

Cf. A046392, A002385, A069217, A032350, A030229, A075800, A075805 (first differences).

test := proc(n) local d; d := convert(n,base,10); return ListTools[Reverse](d)=d and numtheory[mobius](n)=1; end; a := []; for n from 1 to 7000 do if test(n) then a := [op(a),n]; end; od; a;

Select[Range[10000], PalindromeQ[#] && MoebiusMu[#] == 1 &] (* Paolo Xausa, Mar 10 2025 *)

Edited by Dean Hickerson, Oct 21 2002

cp's OEIS Frontend

A046399 Smallest squarefree palindrome with exactly n distinct prime factors.

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