A075048 10-smooth numbers that show their prime factors.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..12.

Example

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.

Prog

(Python)
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

Crossrefs

Cf. A002473, A052382, A067183, A357132.

Sequence in context: A157869 A046705 A054218 * A281021 A230046 A098463

Adjacent sequences: A075045 A075046 A075047 * A075049 A075050 A075051

Keyword

base,fini,full,nonn

Author

Amarnath Murthy, Sep 03 2002

Extensions

Edited by Don Reble, Jun 07 2003

Offset 1 from Alois P. Heinz, Sep 15 2022

Status

approved