A050694 - OEIS

%I #36 Feb 25 2024 05:57:50

%S 25,32,125,128,135,175,243,250,256,324,375,432,512,625,735,875,1024,

%T 1250,1352,1372,1593,1675,1715,1792,2048,2176,2304,2500,2510,2560,

%U 2570,2744,3072,3087,3125,3375,3645,3675,3792,4232,4375,5120,5210,5230,5832

%N Composite numbers k such that all prime factors of k are a substring of k.

%H Charles R Greathouse IV, <a href="/A050694/b050694.txt">Table of n, a(n) for n = 1..10000</a> (first 150 terms from Lava)

%H Gil Broussard, <a href="http://home.mindspring.com/~kikiriki/id14.html">Integers containing prime factors as substrings</a>.

%F a(n) << n log n. - _Charles R Greathouse IV_, Jul 09 2015

%e 1675 = 5*5*67 -> 167{5} and 1{67}5.

%t d[n_]:=IntegerDigits[n]; t={}; Do[le1=Max@@Length/@(t1=d[First/@FactorInteger[n]]); t2=Flatten[Table[Partition[d[n],i,1],{i,le1}],1]; If[!PrimeQ[n]&&Complement[t1,t2]=={},AppendTo[t,n]],{n,20,5850}]; t (* _Jayanta Basu_, May 31 2013 *)

%o (PARI) substr(m,n)=my(a=#Str(m),b=#Str(n)); for(i=0,a-b,if(valuation(m-n,10)>=b, return(1)); m\=10); 0

%o is(n)=if(isprime(n)||n<9, return(0)); my(f=factor(n)[,1]); for(i=1,#f,if(!substr(n,f[i]), return(0))); 1 \\ _Charles R Greathouse IV_, Jul 09 2015

%Y Cf. A050695, A050696, A035140, A050697.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Aug 15 1999