A373467 Palindromes with exactly 7 (distinct) prime divisors.

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

Author

M. F. Hasler, Jun 06 2024

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

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).

Cf. A002113 (palindromes), A176655 (omega(.) = 7), A123321 (products of 7 distinct primes).

Programs

PARI

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}

Formula

Intersection of A002113 and A176655.