%I #21 Nov 19 2022 21:20:06
%S 1,2,3,5,6,7,24,343,375,392,640,686,2401,3375,4802,4913,6400,13122,
%T 14336,14641,30375,33614,64000,468750,640000,1703936,2725888,2839714,
%U 2883584,4687500,5537792,6298560,6400000,7864320,13668750,14172488,19267584,21807104,26040609,28629151
%N Numbers k such that the sum of the distinct digits of k is equal to the product of the prime divisors of k.
%C 64*10^k is a term of the sequence for every positive integer k.
%e 375 = 3*5^3. 3+7+5 = 3*5. Thus 375 is a term.
%t Select[Range[10^6], Plus @@ Union[IntegerDigits[#]] == Times @@ FactorInteger[#][[;;,1]] &] (* _Amiram Eldar_, Sep 21 2022 *)
%o (PARI) isok(k) = vecsum(Set(digits(k))) == vecprod(factor(k)[, 1]);
%o (Python)
%o from math import prod
%o from sympy import primefactors
%o def ok(n): return n and sum(map(int, set(str(n)))) == prod(primefactors(n))
%o print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Sep 22 2022
%Y Cf. A008472, A217928.
%K nonn,base
%O 1,2
%A _Alexandru Petrescu_, Sep 21 2022
%E More terms from _Michel Marcus_, Sep 21 2022