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A348050 Palindromes setting a new record of their number of prime divisors A001222.

%I A348050 #22 Oct 28 2021 17:39:54
%S A348050 1,2,4,8,88,252,2112,4224,8448,44544,48384,405504,4091904,405909504,
%T A348050 677707776,4285005824,21128282112,29142024192,4815463645184,
%U A348050 445488555884544,27874867776847872,40539458585493504,63556806860865536,840261068860162048,4870324782874230784
%N A348050 Palindromes setting a new record of their number of prime divisors A001222.
%t A348050 m=0;lst=Union@Flatten[Table[{FromDigits@Join[s=IntegerDigits@n,Reverse@s],FromDigits@Join[w=IntegerDigits@n,Rest@Reverse@w]},{n,10^5}]];Do[t=PrimeOmega@lst[[n]];If[t>m,Print@lst[[n]];m=t],{n,Length@lst}] (* _Giorgos Kalogeropoulos_, Oct 25 2021 *)
%o A348050 (Python)
%o A348050 from sympy import factorint
%o A348050 from itertools import product
%o A348050 def palsthru(maxdigits):
%o A348050     midrange = [[""], [str(i) for i in range(10)]]
%o A348050     for digits in range(1, maxdigits+1):
%o A348050         for p in product("0123456789", repeat=digits//2):
%o A348050             left = "".join(p)
%o A348050             if len(left) and left[0] == '0': continue
%o A348050             for middle in midrange[digits%2]:
%o A348050                 yield int(left+middle+left[::-1])
%o A348050 def afind(maxdigits):
%o A348050     record = -1
%o A348050     for p in palsthru(maxdigits):
%o A348050         f = factorint(p, multiple=True)
%o A348050         if p > 0 and len(f) > record:
%o A348050             record = len(f)
%o A348050             print(p, end=", ")
%o A348050 afind(10) # _Michael S. Branicky_, Oct 25 2021
%Y A348050 Cf. A001222, A002113, A046399, A335645.
%Y A348050 Cf. A046328, A046329, A046330, A046331, A046332, A046333, A046334, A046335, A046336.
%K A348050 nonn,base
%O A348050 1,2
%A A348050 _Hugo Pfoertner_, Oct 25 2021
%E A348050 a(1) = 1 from _David A. Corneth_, Oct 25 2021
%E A348050 a(16)-a(19) from _Giorgos Kalogeropoulos_, Oct 25 2021
%E A348050 a(20) from _Michael S. Branicky_, Oct 25 2021
%E A348050 a(21)-a(25) from _Chai Wah Wu_, Oct 28 2021