login
Palindromic odd squarefree numbers with an even number of distinct prime factors.
1

%I #14 Jan 05 2025 23:40:48

%S 1,33,55,77,111,141,161,303,323,393,505,515,535,545,565,707,717,737,

%T 767,939,949,959,979,989,1111,1441,1661,1991,3003,3113,3223,3443,3883,

%U 5005,5115,7117,7447,7997,9119,9229,9449,10001,10101,10401,10801,10901

%N Palindromic odd squarefree numbers with an even number of distinct prime factors.

%H Robert Israel, <a href="/A075810/b075810.txt">Table of n, a(n) for n = 1..10000</a>

%e 77=7*11 and 3003=3*7*11*13 are palindromic, odd, squarefree and have an even number of prime factors.

%p 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 11000 by 2 do if test(n) then a := [op(a),n]; end; od; a;

%t psdQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]&&SquareFreeQ[n] && EvenQ[PrimeNu[n]]]; Select[Range[1,11001,2],psdQ] (* _Harvey P. Dale_, Aug 21 2011 *)

%Y Cf. A056913.

%K nonn,base,look

%O 1,2

%A _Jani Melik_, Oct 13 2002

%E Edited by _Dean Hickerson_, Oct 21 2002