A036308 Composite numbers whose prime factors contain no digits other than 1 and 8.

121, 1331, 1991, 8921, 9691, 12991, 14641, 19921, 21901, 32761, 89221, 98131, 106601, 142901, 146791, 159461, 161051, 199991, 213761, 219131, 240911, 327791, 360371, 657721, 714491, 776161, 892991, 957791, 976921, 981431, 1040461, 1079441, 1172611, 1394761, 1468091

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 A020456. - David A. Corneth, Oct 09 2020

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 58 terms from Vincenzo Librandi)
• Index entries for sequences related to prime factors.

Crossrefs

Cf. A020456, A036302-A036325.

Programs

Magma

[n: n in [4..1500000] | not IsPrime(n) and forall{f: f in PrimeDivisors(n) | Intseq(f) subset [1,8]}]; // Bruno Berselli, Aug 26 2013

Mathematica

dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[FactorInteger[n]][[1]]]]}, !PrimeQ[n]&&(d == {1}||d == {8}||d == {1, 8})]; Select[Range[2, 1500000], dpfQ] (* Vincenzo Librandi, Aug 25 2013 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020456} (p/(p - 1)) - Sum_{p in A020456} 1/p - 1 = 0.0101097220... . - Amiram Eldar, May 18 2022

Extensions

More terms from Vincenzo Librandi, Aug 25 2013