A369209 Numbers whose number of divisors has the largest prime factor 3.

4, 9, 12, 18, 20, 25, 28, 32, 36, 44, 45, 49, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 96, 98, 99, 100, 108, 116, 117, 121, 124, 126, 132, 140, 147, 148, 150, 153, 156, 160, 164, 169, 171, 172, 175, 180, 188, 196, 198, 200, 204, 207, 212, 220, 224, 225, 228

Offset: 1

Author

Amiram Eldar, Jan 16 2024

Keywords

• nonn
• easy

Comments

Subsequence of A059269 and first differs from it at n = 36: A059269(136) = 44 has 15 = 3 * 5 divisors and thus is not a term of this sequence.

Numbers k such that A000005(k) is in A065119.

Numbers k such that A071188(k) = 3.

Equals the complement of A354181, without the terms of A036537 (i.e., complement(A354181) \ A036537).

The asymptotic density of this sequence is Product_{p prime} (1-1/p) * (Sum_{k>=1} 1/p^(A003586(k)-1)) - A327839 = 0.26087647470200496716... .

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A003586, A006530, A036537, A065119, A336595, A071188, A211337, A211338, A327839, A354181.

Subsequence of A013929 and A059269.

Subsequences: A001248, A030627, A050997, A054753, A062503, A067259, A079395, A085986, A085987, A086975, A095990, A096156, A138032, A162143, A179643, A179645.

Programs

Mathematica

gpf[n_] := FactorInteger[n][[-1, 1]]; Select[Range[300], gpf[DivisorSigma[0, #]] == 3 &]

PARI

gpf(n) = if(n == 1, 1, vecmax(factor(n)[, 1]));
is(n) = gpf(numdiv(n)) == 3;