A046396 Palindromes which are the product of 6 distinct primes.

222222, 282282, 474474, 555555, 606606, 646646, 969969, 2040402, 2065602, 2206022, 2417142, 2646462, 2673762, 2875782, 3262623, 3309033, 4179714, 4192914, 4356534, 4585854, 4912194, 5021205, 5169615, 5174715, 5578755

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Comments

The original definition "Palindromes with exactly 6 distinct prime factors" was misleading. For example, the number 414414 = 2 * 3^2 * 7 * 11 * 13 * 23 has exactly 6 distinct prime factors, although the factor 3 occurs twice. But the listed terms show that it is not in this sequence. See sequence A373466 for the variant corresponding to that definition. - M. F. Hasler, Jun 06 2024

Crossrefs

Cf. A046332 (similar, but for 6 prime factors counted with multiplicity).

Cf. A002113 (palindromes), A067885 (products of 6 distinct primes).

Cf. A074969 (numbers having 6 distinct prime divisors).

Programs

Mathematica

Select[Range[6*10^6],#==IntegerReverse[#]&&PrimeNu[#]==PrimeOmega[#]==6&] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Mar 17 2016 *)

PARI

A046332_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && issquarefree(start) && listput(L, start)); L} \\ M. F. Hasler, Jun 06 2024

Formula

Intersection of A002113 and A067885. - M. F. Hasler, Jun 06 2024

Extensions

Name edited