

A036319


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


3



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
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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, A036302A036325.
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



