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

1,1

Comments

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

Links

Table of n, a(n) for n=1..44.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A070275, A217928.

Sequence in context: A029976 A074310 A264576 * A070275 A171042 A068827

Adjacent sequences: A356978 A356979 A356980 * A356982 A356983 A356984

Keyword

nonn,base

Author

Tanya Khovanova, Sep 09 2022

Status

approved