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

1,1

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.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A050695, A050696, A035140, A050697.

Sequence in context: A263029 A225418 A035140 * A107608 A219951 A209333

Adjacent sequences: A050691 A050692 A050693 * A050695 A050696 A050697

Keyword

nonn,base

Author

Patrick De Geest, Aug 15 1999

Status

approved