A036311 Composite numbers whose prime factors contain no digits other than 2 and 5.

4, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• easy
• base

Comments

A003592 with 1, 2 and 5 removed. - Robert Israel, Apr 29 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..10000 (first 131 terms from Vincenzo Librandi)
• Index entries for sequences related to prime factors.

Crossrefs

Cf. A003592, A036302-A036325, A025612.

Programs

Magma

[n: n in [4..13000] | not IsPrime(n) and forall{f: f in PrimeDivisors(n) | Intseq(f) subset [2,5]}]; // Bruno Berselli, Aug 26 2013

Maple

N:= 20000: # to get all terms <= N
S:= {seq(seq(2^i*5^j,i=0..ilog2(N/5^j)),j=0..floor(log[5](N)))} minus {1,2,5}:
sort(convert(S,list)); # Robert Israel, Apr 29 2018

Mathematica

dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[FactorInteger[n]][[1]]]]}, !PrimeQ[n]&&(d == {2}||d == {5}||d == {2, 5})]; Select[Range[15000], dpfQ] (* Vincenzo Librandi, Aug 25 2013 *)

Formula

Sum_{n>=1} 1/a(n) = 4/5. - Amiram Eldar, May 18 2022~