A036318 Composite numbers whose prime factors contain no digits other than 4 and 7.

49, 329, 343, 2209, 2303, 2401, 15463, 16121, 16807, 31129, 52339, 103823, 108241, 112847, 117649, 209009, 217903, 313439, 334439, 351419, 366373, 523229, 542129, 542339, 544229, 726761, 757687, 789929, 823543, 1463063, 1525321, 2104519

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• easy
• base

Comments

All terms are a product of at least two terms of A020465. - David A. Corneth, Oct 09 2020

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Index entries sequences related to prime factors.

Crossrefs

Cf. A020465, A036302-A036325.

Programs

Mathematica

pf47Q[n_]:=Module[{u=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},!PrimeQ[n]&&(u=={4}||u=={7}||u=={4,7})];Select[ Range[ 2200000],pf47Q] (* Harvey P. Dale, Jun 05 2013 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020465} (p/(p - 1)) - Sum_{p in A020465} 1/p - 1 = 0.0279830135... . - Amiram Eldar, May 22 2022