A039700 Numbers k such that the largest power of 3 dividing k equals 3^omega(k).

1, 3, 18, 36, 45, 63, 72, 99, 117, 144, 153, 171, 207, 225, 261, 270, 279, 288, 333, 369, 378, 387, 423, 441, 477, 531, 540, 549, 576, 594, 603, 639, 657, 702, 711, 747, 756, 801, 873, 909, 918, 927, 945, 963, 981, 1017, 1026, 1080, 1089, 1125, 1143, 1152

Offset

1,2

Comments

Here, "omega(k)" means the number of prime factors of k counted without multiplicity. - Harvey P. Dale, Sep 30 2015

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Example

omega(18) = 2 and 9 = 3^2 is the largest power of 3 dividing 18, hence 18 is in the sequence.

Mathematica

Select[Range[1200], IntegerExponent[#, 3]==PrimeNu[#]&] (* Harvey P. Dale, Sep 30 2015 *)

Prog

(PARI) isok(k) = valuation(k, 3) == omega(k); \\ Amiram Eldar, Apr 26 2025

Crossrefs

Cf. A001221 (omega), A038500, A023534 (similar for powers of 2).

Sequence in context: A125284 A372707 A097989 * A069147 A337921 A365442

Adjacent sequences: A039697 A039698 A039699 * A039701 A039702 A039703

Keyword

nonn

Author

Benoit Cloitre, Sep 04 2002

Status

approved