%I #28 Mar 25 2024 12:05:45

%S 1,16,128,250,480,864,21600,62208,73728

%N Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 7.

%C There is a finite number of such numbers; we only calculated the terms in [1, 10^10] (Property 1' of Clerc).

%H René-Louis Clerc, <a href="https://hal.science/hal-04235744">Quelques nombres de Niven-Harshad particuliers</a>, 2023.

%H René-Louis Clerc, <a href="https://ut3-toulouseinp.hal.science/hal-04507547">Nombres S+P, maxSP, minSP et |P-S|</a>, hal-04507547 [math.nt], 2024. (In French)

%e 21600 = 116655_7, (1+1+6+6+5+5)*(1*1*6*6*5*5) = 24*900 = 21600.

%t Select[Range[7^7], #1 == Times @@ DeleteCases[#2, 0]*Total[#2] & @@ {#, IntegerDigits[#, 7]} &] (* _Michael De Vlieger_, Mar 25 2024 *)

%o (PARI) isok(k, b) = my(d=select(x->(x>0), digits(k,b))); vecprod(d)*vecsum(d) == k;

%o for (k=1, 10^5, if (isok(k, 7), print1(k, ", ")))

%Y Cf. A066282, A062331, A023651, A038364, A038369, A062237.

%K base,nonn,fini,more

%O 1,2

%A _René-Louis Clerc_, Jan 10 2024