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

1,1

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A035139, A035140.

Sequence in context: A241754 A063365 A116869 * A205222 A116154 A305067

Adjacent sequences: A035138 A035139 A035140 * A035142 A035143 A035144

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 1998

Extensions

Definition corrected by Charles R Greathouse IV, May 02 2013

Status

approved