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A329100
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Composite palindromes whose divisors > 1 are all nontrivial palindromes (i.e., palindromes with at least two digits).
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1
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121, 1111, 1331, 1441, 1661, 1991, 3443, 3883, 7997, 10201, 12221, 13231, 14641, 15251, 15851, 18281, 19291, 31613, 35653, 37673, 37873, 38683, 112211, 113311, 115511, 116611, 124421, 125521, 134431, 136631, 139931, 145541, 146641, 157751, 167761, 169961, 176671
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OFFSET
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1,1
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COMMENTS
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All terms start and end with the digits 1,3,7 or 9.
First term with 3 prime factors: 1331 = 11^3.
First term with 3 distinct prime factors: 145541 = 11*101*131.
First term with 4 prime factors: 14641 = 11^4.
First term with 5 prime factors: 1478741 = 11^4*101.
No term with more than 3 distinct prime factors or more than 5 prime factors among first 10000 terms.
(End)
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LINKS
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EXAMPLE
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For k = 1331, its divisors > 1 are 11, 121 and 1331, all of which are palindromes with at least two digits, so 1331 is a term.
For k = 167761, its divisors > 1 are 11, 101, 151, 1111, 1661, 15251 and 167761, all of which are palindromes with at least two digits, so 167761 is a term.
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MATHEMATICA
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aQ[n_] := CompositeQ[n] && AllTrue[Rest @ Divisors[n], # > 10 && PalindromeQ @ IntegerDigits[#] &]; Select[Range[200000], aQ] (* Amiram Eldar, Nov 06 2019 *)
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PROG
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(PARI) isA329100(n) = if((n>1) && !isprime(n) && gcd(n, 210)==1, {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d == rd); }, 0) \\ Jianing Song, Nov 06 2019, based on the program of A062687
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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