A067183 - OEIS

%I #26 Sep 15 2022 15:59:33

%S 1,2,3,5,6,7,135,175,735,1176,1715,131712

%N Product of the prime factors of n equals the product of the digits of n.

%C Terms are zeroless 7-smooth numbers (cf. A238985). - _David A. Corneth_, Sep 14 2022

%e The prime factors of 1176 are 2,3,7 which have product = 42, the product of the digits of 1176, so 1176 is a term of the sequence.

%t Do[ If[ Apply[ Times, Transpose[ FactorInteger[n]] [[1]] ] == Apply[ Times, IntegerDigits[n]], Print[n]], {n, 2, 2*10^7} ]

%t Select[Range[2,1000000],Times@@Transpose[FactorInteger[#]][[1]] == Times@@ IntegerDigits[#]&] (* _Harvey P. Dale_, Mar 19 2012 *)

%o (PARI) is(n) = {if(n == 1, return(1)); my(f = factor(n, 7), d = digits(n)); if(f[#f~, 1] > 7, return(0)); vecprod(f[,1]) == vecprod(d)} \\ _David A. Corneth_, Sep 14 2022

%Y Cf. A002473, A006753, A052382, A075048, A238985, A357132.

%K nonn,base,fini,full

%O 1,2

%A _Joseph L. Pe_, Feb 18 2002

%E Edited and extended by _Robert G. Wilson v_, Feb 19 2002

%E a(1)=1 inserted by _Alois P. Heinz_, Sep 14 2022