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
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.
Programs
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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