A356981 Numbers k such that the sum of distinct digits of k equals the sum of the prime divisors of k.

2, 3, 5, 7, 84, 144, 160, 250, 343, 468, 735, 936, 975, 1125, 1215, 1375, 1408, 1600, 1694, 1872, 2401, 2500, 2646, 2880, 3920, 4913, 6084, 6318, 6860, 7296, 7695, 8624, 8704, 8788, 9126, 10125, 10240, 10816, 11264, 12672, 12675, 14641, 14896, 16000

Offset: 1

Author

Tanya Khovanova, Sep 09 2022

Keywords

• nonn
• base

Comments

Similar to A070275, where distinctness of digits is not required.

Examples

			144 = 2^4*3^2 and 1+4=2+3. Thus, 144 is in this sequence.
		

Crossrefs

Cf. A070275, A217928.

Programs

Mathematica

Select[Range[2, 20000],Total[Union[IntegerDigits[#]]] ==  Total[Transpose[FactorInteger[#]][[1]]] &]

PARI

isok(k) = vecsum(Set(digits(k))) == vecsum(factor(k)[, 1]); \\ Michel Marcus, Sep 12 2022

Python

from itertools import count, islice
from sympy import primefactors
def A356981_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k:sum(int(d) for d in set(str(k)))==sum(primefactors(k)), count(max(startvalue,1)))
A356981_list = list(islice(A356981_gen(),30)) # Chai Wah Wu, Sep 12 2022