A121342 Composite numbers that are a concatenation of their distinct prime divisors in some order.

735, 3792, 1341275, 13115375, 22940075, 29373375, 71624133, 311997175, 319953792, 1019127375, 1147983375, 1734009275, 5581625072, 7350032375, 17370159615, 33061224492, 103375535837, 171167303912, 319383665913, 533671737975, 2118067737975, 3111368374257

Offset: 1

Author

Tanya Khovanova, Aug 28 2006

Keywords

• base
• nonn

Comments

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).

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..30

Crossrefs

Cf. A083359, A083360, A083361, A096595.

Programs

Mathematica

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 *)

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

Extensions

a(14) from Emmanuel Vantieghem, Nov 30 2016

Missing term 5581625072=5581||62507||2 inserted by Deron Stewart, Feb 15 2019

a(16)-a(22) from Giovanni Resta, Mar 04 2019