A373466 Palindromes with exactly 6 distinct prime divisors.

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

Offset: 1

Author

M. F. Hasler, Jun 06 2024

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A002113 (palindromes), A074969 (omega(.) = 6).

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).

Programs

Mathematica

Select[Range[3000000],PalindromeQ[#]&&Length[FactorInteger[#]]==6&] (* James C. McMahon, Jun 08 2024 *)

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}

Formula

Intersection of A002113 and A074969.