A067183 -id:A067183 - cp's OEIS frontend

A075048 10-smooth numbers that show their prime factors.

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

A357132 Numbers k such that the product of distinct digits of k equals the product of the prime divisors of k.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 135, 175, 735, 1176, 1715, 13122, 131712, 2333772

Offset: 1

Alexandru Petrescu, Sep 14 2022

			175 = 5^2*7, 1*7*5 = 5*7. Thus 175 is a term.

Cf. A002473, A052382, A067183, A075048, A238985, A356981.

Select[Range[2400000], Times@@DeleteDuplicates[IntegerDigits[#]] == Times@@First/@FactorInteger[#] &] (* Stefano Spezia, Apr 25 2024 *)

isok(k) = vecprod(Set(digits(k))) == vecprod(factor(k)[, 1]);

cp's OEIS Frontend

A075048 10-smooth numbers that show their prime factors.

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