A036319 Composite numbers whose prime factors have no digits other than 4's and 9's.

201601, 224051, 249001, 2244551, 2494501, 4467101, 4964551, 19957601, 22180051, 22225051, 22449551, 24700001, 24949501, 24990001, 42632101, 42654551, 47379551, 47404501, 49735051, 90518849, 98982601, 100598899, 111801449, 124251499, 199557601, 221780051, 222200551, 247445501

Offset

1,1

Comments

Closed under multiplication. - David A. Corneth, Sep 21 2020

From M. F. Hasler, Sep 22 2020: (Start)

Also closed under LCM, but not under GCD.

All terms are congruent to 1 or 9 (mod 10), depending on the parity of their number of prime factors counted with multiplicity, A001222. (End)

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Index entries for sequences related to prime factors.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020466} (p/(p - 1)) - Sum_{p in A020466} 1/p - 1 = 0.00001523788893... . - Amiram Eldar, May 22 2022

Example

The smallest prime made up of 4's and 9's is 449 (see A020466), so the smallest term here is 449^2 = 201601. - N. J. A. Sloane, Sep 21 2020

Mathematica

cn49Q[n_]:=Module[{fi=FactorInteger[n][[All, 1]]}, CompositeQ[n]&&Union[ Flatten[ IntegerDigits/@fi]]=={4, 9}&&AllTrue[fi, PrimeQ]]; Select[Range[ 1, 1006*10^5, 2], cn49Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2020 *)

Prog

(PARI) is(N)={!isprime(N)&& !#setminus(Set(concat(apply (digits, factor(N)[, 1]))), [4, 9])} \\ M. F. Hasler, Sep 22 2020

Crossrefs

Cf. A001222, A020466, A036302-A036325.

Sequence in context: A202316 A186958 A184406 * A241060 A233845 A233846

Adjacent sequences: A036316 A036317 A036318 * A036320 A036321 A036322

Keyword

nonn,easy,base

Author

Patrick De Geest, Dec 15 1998

Extensions

More terms from David A. Corneth, Sep 21 2020

Status

approved