A176359 Numbers with at least three 3s in their prime signature.

27000, 74088, 189000, 287496, 297000, 343000, 351000, 370440, 459000, 474552, 513000, 621000, 783000, 814968, 837000, 963144, 999000, 1029000, 1061208, 1107000, 1157625, 1161000, 1259496, 1269000, 1323000, 1331000, 1407672, 1431000, 1437480, 1481544, 1593000, 1647000, 1704024, 1809000, 1852200, 1917000, 1971000, 2012472, 2079000, 2133000, 2148552

Offset

1,1

Comments

In other words, if the canonical prime factorization of a term into prime powers is Product p(i)^e(i), then e(i) = 3 for at least three values of i.

The asymptotic density of this sequence is 1 - (1 + s(1) + s(1)^2/2 - s(2)/2) * Product_{p prime} (1-1/p^3+1/p^4) = 0.000018992895371889141564..., where s(k) = Sum_{p prime} ((p-1)/(p^4-p+1))^k. - Amiram Eldar, Jul 22 2024

Links

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

Example

27000 is a term since 27000 = 2^3 * 3^3 * 5^3.
74088 is a term since 74088 = 2^3 * 5^3 * 7^3.

Mathematica

f[n_]:=Count[Last/@FactorInteger[n], 3]>2; Select[Range[10!], f]

Prog

(PARI) is(n) = #select(x -> x == 3, factor(n)[, 2]) > 2; \\ Amiram Eldar, Jul 22 2024

Crossrefs

Cf. A000578, A001235, A176297, A176313, A176350.

Subsequence of A109399.

Sequence in context: A227348 A391755 A386802 * A162144 A305728 A253485

Adjacent sequences: A176356 A176357 A176358 * A176360 A176361 A176362

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 07 2010

Extensions

Edited by Matthew Vandermast, Dec 09 2010

Status

approved