A357263 Numbers k such that the sum of the distinct digits of k is equal to the product of the prime divisors of k.

1, 2, 3, 5, 6, 7, 24, 343, 375, 392, 640, 686, 2401, 3375, 4802, 4913, 6400, 13122, 14336, 14641, 30375, 33614, 64000, 468750, 640000, 1703936, 2725888, 2839714, 2883584, 4687500, 5537792, 6298560, 6400000, 7864320, 13668750, 14172488, 19267584, 21807104, 26040609, 28629151

Offset: 1

Author

Alexandru Petrescu, Sep 21 2022

Keywords

• nonn
• base

Comments

64*10^k is a term of the sequence for every positive integer k.

Examples

			375 = 3*5^3. 3+7+5 = 3*5. Thus 375 is a term.
		

Crossrefs

Cf. A008472, A217928.

Programs

Mathematica

Select[Range[10^6], Plus @@ Union[IntegerDigits[#]] == Times @@ FactorInteger[#][[;;,1]] &] (* Amiram Eldar, Sep 21 2022 *)

PARI

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

Python

from math import prod
from sympy import primefactors
def ok(n): return n and sum(map(int, set(str(n)))) == prod(primefactors(n))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 22 2022

Extensions

More terms from Michel Marcus, Sep 21 2022