A035141 Composite numbers k such that digits in k and in juxtaposition of prime factors of k are the same (apart from multiplicity).

132, 312, 735, 1255, 1377, 1775, 1972, 3792, 4371, 4773, 5192, 6769, 7112, 7236, 7371, 7539, 9321, 11009, 11099, 11132, 11163, 11232, 11255, 11375, 11913, 12176, 12326, 12595, 12955, 13092, 13175, 13312, 13377, 13491, 13755, 14842, 15033

Offset: 1

Author

Patrick De Geest, Nov 15 1998

Keywords

• nonn
• base

Examples

			1972 = {1,2,7,9} -> 2 * 2 * 17 * 29, so 1972 is a term.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A035139, A035140.

Programs

Mathematica

Fac[n_]:=Sort[DeleteDuplicates[Flatten[IntegerDigits[Take[FactorInteger[n], All,1]]]]];Fn[n_]:=Sort[DeleteDuplicates[IntegerDigits[n]]];t={};Do[If[! PrimeQ[n]&&Fac[n]===Fn[n],AppendTo[t, n]],{n,2,15100}];t (* Jayanta Basu, May 02 2013 *)

PARI

is(n)=if(isprime(n)||n<9,return(0));my(f=factor(n)[,1],v=[]);for(i=1,#f,v=concat(v,digits(f[i])));vecsort(digits(n),,8)==vecsort(v,,8) \\ Charles R Greathouse IV, May 02 2013

Formula

a(n) ~ n. Proof: the density of numbers without a given decimal digit in their prime factors is 0, which can be seen by looking at the first (or second, in the case of 0) digit and removing all primes with that digit. Taken with the 0 density of numbers missing any decimal digit the result is obtained. - Charles R Greathouse IV, May 02 2013

Extensions

Definition corrected by Charles R Greathouse IV, May 02 2013