A046399
Smallest squarefree palindrome with exactly n distinct prime factors.
Original entry on oeis.org
1, 2, 6, 66, 858, 6006, 222222, 22444422, 244868442, 6434774346, 438024420834, 50146955964105, 2415957997595142, 495677121121776594, 22181673755737618122, 5521159517777159511255, 477552751050050157255774
Offset: 0
- J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), p. 315, Pour la Science, Paris 2000.
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r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[k = 1; While[r[k] != k || !SquareFreeQ[k] || Length[Select[Divisors[k], PrimeQ]] != n, k++ ]; Print[k], {n, 0, 30}] (* Ryan Propper, Sep 16 2005 *)
A373467
Palindromes with exactly 7 (distinct) prime divisors.
Original entry on oeis.org
20522502, 21033012, 22444422, 23555532, 24266242, 25777752, 26588562, 35888853, 36399363, 41555514, 41855814, 42066024, 43477434, 43777734, 44888844, 45999954, 47199174, 51066015, 51666615, 52777725, 53588535, 53888835, 55233255, 59911995, 60066006, 60366306, 61777716, 62588526, 62700726
Offset: 1
Obviously all terms must be palindromic; let us consider the prime factorization:
a(1) = 20522502 = 2 * 3^2 * 7 * 11 * 13 * 17 * 67 has exactly 7 distinct prime divisors, although the factor 3 appears twice in the factorization. (Without the second factor 3 the number would not be palindromic.)
a(2) = 21033012 = 2^2 * 3 * 7 * 11 * 13 * 17 * 103 has exactly 7 distinct prime divisors, although the factor 2 appears twice in the factorization. (Without the second factor 2 the number would not be palindromic.)
a(3) = 22444422 = 2 * 3 * 7 * 11 * 13 * 37 * 101 is the product of 7 distinct primes (cf. A123321), hence the first squarefree term of this sequence.
Cf.
A046333 (same with bigomega = 7: counting prime factors with multiplicity),
A046397 (same but only squarefree terms),
A373465 (same with omega = 5),
A046396 (same with omega = 6).
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A373467_upto(N, start=vecprod(primes(7)), num_fact=7)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && listput(L, start)); L}
Showing 1-2 of 2 results.
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