A036316 Composite numbers whose prime factors contain no digits other than 3 and 7.

9, 21, 27, 49, 63, 81, 111, 147, 189, 219, 243, 259, 333, 343, 441, 511, 567, 657, 729, 777, 999, 1011, 1029, 1119, 1323, 1369, 1533, 1701, 1813, 1971, 2187, 2199, 2319, 2331, 2359, 2401, 2611, 2701, 2997, 3033, 3087, 3357, 3577, 3969, 4107, 4599, 5103

Offset

1,1

Comments

All terms are a product of at least two terms of A020463. - David A. Corneth, Oct 09 2020

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 800 terms from Vincenzo Librandi)

Index entries for sequences related to prime factors.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020463} (p/(p - 1)) - Sum_{p in A020463} 1/p - 1 = 0.3143000293... . - Amiram Eldar, May 22 2022

Mathematica

dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[FactorInteger[n]][[1]]]]}, !PrimeQ[n]&&(d == {3}||d == {7}||d == {3, 7})]; Select[Range[6000], dpfQ] (* Vincenzo Librandi, Aug 25 2013 *)

Prog

(Magma) [n: n in [9..6000] | not IsPrime(n) and forall{f: f in PrimeDivisors(n) | Intseq(f) subset [3, 7]}]; // Bruno Berselli, Aug 26 2013

Crossrefs

Cf. A003594, A020463, A036302-A036325.

Sequence in context: A186815 A106214 A348839 * A340122 A339728 A267216

Adjacent sequences: A036313 A036314 A036315 * A036317 A036318 A036319

Keyword

nonn,easy,base

Author

Patrick De Geest, Dec 15 1998

Status

approved