A121342 - OEIS

%I #31 Mar 04 2019 09:47:06

%S 735,3792,1341275,13115375,22940075,29373375,71624133,311997175,

%T 319953792,1019127375,1147983375,1734009275,5581625072,7350032375,

%U 17370159615,33061224492,103375535837,171167303912,319383665913,533671737975,2118067737975,3111368374257

%N Composite numbers that are a concatenation of their distinct prime divisors in some order.

%C Larger terms of this sequence were calculated by _Giovanni Resta_ and _Farideh Firoozbakht_. This sequence is a subsequence of A083360 (Subsequence of sequence A083359 in which factors do not overlap in the number), which is a subsequence of A083359 (Visible Factor Numbers, or VPNs: numbers n with the property that every prime factor of n can be found in the decimal expansion of n and every digit of n can be found in a prime factor. No additional 0's and 1's are allowed). Also, this sequence is a subsequence of A096595 (Numbers n with the property that n is an anagram of the digits of the distinct prime factors of n).

%H Giovanni Resta, <a href="/A121342/b121342.txt">Table of n, a(n) for n = 1..30</a>

%e For example: 735 = 3*5*7^2 and 3792 = 2^4*3*79.

%t fQ[n_] := !PrimeQ@n && MemberQ[ FromDigits /@ (Flatten@# & /@ IntegerDigits[ Permutations[ First /@ FactorInteger@n]]), n]; Do[ If[fQ@n, Print@n], {n, 10^7/4}] (* _Robert G. Wilson v_, Sep 02 2006 *)

%o (PARI) isok(n) = {if (isprime(n), return (0)); my(vp = factor(n)[,1], nb = #vp); for (i=0, nb!-1, my(vperm = numtoperm(nb, i), s = ""); for (i=1, #vperm, s = concat(s, vp[vperm[i]]);); if (eval(s) == n, return (1));); return (0);} \\ _Michel Marcus_, Feb 19 2019

%Y Cf. A083359, A083360, A083361, A096595.

%K base,nonn

%O 1,1

%A _Tanya Khovanova_, Aug 28 2006

%E a(14) from _Emmanuel Vantieghem_, Nov 30 2016

%E Missing term 5581625072=5581||62507||2 inserted by _Deron Stewart_, Feb 15 2019

%E a(16)-a(22) from _Giovanni Resta_, Mar 04 2019