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A356750 Palindromic odd numbers with an odd number of distinct prime factors.

%I A356750 #24 Sep 14 2022 08:25:41
%S A356750 3,5,7,9,11,101,121,131,151,181,191,313,343,353,373,383,525,555,585,
%T A356750 595,727,757,777,787,797,919,929,969,1001,1221,1331,1551,1771,1881,
%U A356750 3333,3553,3663,5225,5335,5445,5555,5665,5885,5995,7007,7227,7337,7557,7667,7777,7887,9339,9669,9779,9889,9999,10201,10301
%N A356750 Palindromic odd numbers with an odd number of distinct prime factors.
%C A356750 Numbers in this sequence can be divided by nontrivial prime powers.
%C A356750 This sequence contains palindromic primes: A002385.
%C A356750 This sequence contains palindromic odd composite numbers that are products of an odd number of distinct primes: A075808.
%H A356750 Michael S. Branicky, <a href="/A356750/b356750.txt">Table of n, a(n) for n = 1..10000</a>
%e A356750 Number 525 = 3*5^2*7 has 3 prime factors 3, 5, and 7. Thus, it is in the sequence.
%t A356750 Select[Range[2,12000], OddQ[#] && PalindromeQ[#] && OddQ[Length[Transpose[FactorInteger[#]][[2]]]] &]
%o A356750 (Python)
%o A356750 from sympy import isprime, factorint
%o A356750 from itertools import count, islice, product
%o A356750 def cond(n): return n&1 and (isprime(n) or len(factorint(n))&1)
%o A356750 def oddpals(): # generator of odd palindromes
%o A356750     yield from [1, 3, 5, 7, 9]
%o A356750     for d in count(2):
%o A356750         for first in "13579":
%o A356750             for p in product("0123456789", repeat=(d-2)//2):
%o A356750                 left = "".join(p); right = left[::-1]
%o A356750                 for mid in [[""], "0123456789"][d%2]:
%o A356750                     yield int(first + left + mid + right + first)
%o A356750 def agen(): yield from filter(cond, oddpals())
%o A356750 print(list(islice(agen(), 58))) # _Michael S. Branicky_, Aug 25 2022
%o A356750 (PARI) ispal(n) = my(d1=digits(n)); d1 == Vecrev(d1)
%o A356750 forstep(k=3,10^6,2,if(ispal(k)&&omega(k)%2==1,print1(k,", "))) \\ _Alexandru Petrescu_, Sep 10 2022
%K A356750 nonn,base
%O A356750 1,1
%A A356750 _Tanya Khovanova_, Aug 25 2022