A036303 Composite numbers whose prime factors contain no digits other than 1 and 3.

9, 27, 33, 39, 81, 93, 99, 117, 121, 143, 169, 243, 279, 297, 339, 341, 351, 363, 393, 403, 429, 507, 729, 837, 891, 933, 939, 961, 993, 1017, 1023, 1053, 1089, 1179, 1209, 1243, 1287, 1331, 1441, 1469, 1521, 1573, 1703, 1859, 2187, 2197, 2511, 2673, 2799

Offset

1,1

Comments

All terms are a product of at least two terms of A020451. - David A. Corneth, Oct 09 2020

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Alois P. Heinz)

Index entries for sequences related to prime factors.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020451} (p/(p - 1)) - Sum_{p in A020451} 1/p - 1 = 0.3374936085... . - Amiram Eldar, May 18 2022

Example

The composite 117 = 3^2 * 13 is in the sequence as the digits of the prime factors are either 1 or 3. - David A. Corneth, Oct 17 2020

Mathematica

Select[Range[3000], CompositeQ[#]&&SubsetQ[{1, 3}, Union[Flatten[IntegerDigits/@FactorInteger[#][[;; , 1]]]]]&] (* Harvey P. Dale, Jan 08 2025 *)

Prog

(Python)
from sympy import factorint
def ok(n):
    f = factorint(n)
    return sum(f.values()) > 1 and all(set(str(p)) <= set("13") for p in f)
print(list(filter(ok, range(2800)))) # Michael S. Branicky, Sep 27 2021

Crossrefs

Cf. A003597, A020451, A036302-A036325.

Sequence in context: A108107 A340237 A216168 * A359030 A325299 A353238

Adjacent sequences: A036300 A036301 A036302 * A036304 A036305 A036306

Keyword

nonn,easy,base

Author

Patrick De Geest, Dec 15 1998

Status

approved