login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers n with property that every digit is a prime factor of n.
2

%I #25 Apr 18 2020 00:43:01

%S 2,3,5,7,22,33,55,77,222,333,555,735,777,2222,2232,2322,2772,3222,

%T 3333,3555,5355,5535,5555,5775,7777,22222,22332,22722,23232,23322,

%U 23772,27272,32232,32322,33222,33333,33555,35355,35535,37737,53355,53535

%N Numbers n with property that every digit is a prime factor of n.

%C This is a regular language in base 10. Almost all members of this sequence are multiples of either 42 or 105. There are about 2/63 * 3^n members of this sequence up to 10^n. - _Charles R Greathouse IV_, Nov 09 2011

%H Harry J. Smith and Charles R Greathouse IV, <a href="/A062239/b062239.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Smith)

%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>

%e 77322 is divisible by 7, 3 and 2.

%t Select[Range[2, 50000], Complement[IntegerDigits[#], FactorInteger[#][[All, 1]]] == {} &] (* _Alonso del Arte_, Dec 05 2011 *)

%o (PARI) { n=0; for (m=1, 10^10, t=m; b=1; while (t>0, d=t%10; t=(t-d)/10; if (!isprime(d) || m%d, b=0; break)); if (b, write("b062239.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 17 2010

%K base,easy,nonn

%O 1,1

%A _Erich Friedman_, Jun 30 2001