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

1,1

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.

Links

Table of n, a(n) for n=1..29.

Formula

Intersection of A002113 and A074969.

Example

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.

Mathematica

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

Prog

(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}

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).

Sequence in context: A254509 A254516 A254816 * A046396 A083640 A253990

Adjacent sequences: A373463 A373464 A373465 * A373467 A373468 A373469

Keyword

nonn,base

Author

M. F. Hasler, Jun 06 2024

Status

approved