A050694 Composite numbers k such that all prime factors of k are a substring of k.

25, 32, 125, 128, 135, 175, 243, 250, 256, 324, 375, 432, 512, 625, 735, 875, 1024, 1250, 1352, 1372, 1593, 1675, 1715, 1792, 2048, 2176, 2304, 2500, 2510, 2560, 2570, 2744, 3072, 3087, 3125, 3375, 3645, 3675, 3792, 4232, 4375, 5120, 5210, 5230, 5832

Offset: 1

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn
• base

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 150 terms from Lava)
• Gil Broussard, Integers containing prime factors as substrings.

Crossrefs

Cf. A050695, A050696, A035140, A050697.

Programs

Mathematica

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 *)

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
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

Formula

a(n) << n log n. - Charles R Greathouse IV, Jul 09 2015