A357132 -id:A357132 - cp's OEIS frontend

A067183 Product of the prime factors of n equals the product of the digits of n.

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

Offset: 1

Joseph L. Pe, Feb 18 2002

Terms are zeroless 7-smooth numbers (cf. A238985). - David A. Corneth, Sep 14 2022

			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.

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

Do[ If[ Apply[ Times, Transpose[ FactorInteger[n]] [[1]] ] == Apply[ Times, IntegerDigits[n]], Print[n]], {n, 2, 2*10^7} ]
Select[Range[2,1000000],Times@@Transpose[FactorInteger[#]][[1]] == Times@@ IntegerDigits[#]&] (* Harvey P. Dale, Mar 19 2012 *)

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

Edited and extended by Robert G. Wilson v, Feb 19 2002

a(1)=1 inserted by Alois P. Heinz, Sep 14 2022

A075048 10-smooth numbers that show their prime factors.

Original entry on oeis.org

1, 2, 3, 5, 7, 135, 175, 735, 1715, 13122, 131712, 2333772

Offset: 1

Amarnath Murthy, Sep 03 2002

A number n is in the sequence if it has only noncomposite digits (1,2,3,5,7) and a prime p divides n if and only if p is a digit of n.
No other terms below 10^13.
No more terms < 10^100. - David Wasserman, Jan 04 2005
No more terms < 10^238. - Michael S. Branicky, Jul 03 2022

			131712 is a member because 131712 = 2*2*2*2*2*2*2*3*7*7*7; the prime factors are digits and the digits are factors.

Cf. A002473, A052382, A067183, A357132.

from sympy import primefactors
def ok(n):
    digset = set(map(int, str(n)))
    if not digset <= {1, 2, 3, 5, 7}: return False
    return set(primefactors(n)) == digset - {1}
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Jul 03 2022

Edited by Don Reble, Jun 07 2003

Offset 1 from Alois P. Heinz, Sep 15 2022

cp's OEIS Frontend

A067183 Product of the prime factors of n equals the product of the digits of n.

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