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

1,1

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

Mathematica

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

Prog

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

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.

Sequence in context: A312862 A177880 A059269 * A081619 A336594 A304365

Adjacent sequences: A369206 A369207 A369208 * A369210 A369211 A369212

Keyword

nonn,easy

Author

Amiram Eldar, Jan 16 2024

Status

approved