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A373466
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Palindromes with exactly 6 distinct prime divisors.
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3
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222222, 282282, 414414, 444444, 474474, 555555, 606606, 636636, 646646, 666666, 696696, 828828, 888888, 969969, 2040402, 2065602, 2141412, 2206022, 2343432, 2417142, 2444442, 2572752, 2646462, 2673762, 2747472, 2848482, 2875782, 2949492, 2976792
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OFFSET
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1,1
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COMMENTS
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The term "exactly" clarifies that we don't mean "at least". But the prime divisors may occur to higher powers in the factorization, cf. Examples.
This is different from A046396 which excludes nonsquarefree terms, i.e., terms where one or more of the distinct prime factors occur to a power greater than 1, as it is possible here, cf. Examples.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 222222 = 2 * 3 * 7 * 11 * 13 * 37 has exactly 6 distinct prime divisors.
a(3) = 414414 = 2 * 3^2 * 7 * 11 * 13 * 23 has 6 distinct prime divisors, even though the factor 3 occurs twice in the factorization.
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MATHEMATICA
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Select[Range[3000000], PalindromeQ[#]&&Length[FactorInteger[#]]==6&] (* James C. McMahon, Jun 08 2024 *)
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PROG
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(PARI) A373466_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && listput(L, start)); L}
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CROSSREFS
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Cf. A046332 (same with bigomega = 6: prime factors counted with multiplicity), A046396 (similar, but squarefree terms only), A373465 (same with omega = 5), A373467 (same with bigomega = 7).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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