A035141 - OEIS

%I #21 Jul 30 2021 00:57:24

%S 132,312,735,1255,1377,1775,1972,3792,4371,4773,5192,6769,7112,7236,

%T 7371,7539,9321,11009,11099,11132,11163,11232,11255,11375,11913,12176,

%U 12326,12595,12955,13092,13175,13312,13377,13491,13755,14842,15033

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

%H Charles R Greathouse IV, <a href="/A035141/b035141.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

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

%t 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 *)

%o (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

%Y Cf. A035139, A035140.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 15 1998

%E Definition corrected by _Charles R Greathouse IV_, May 02 2013