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A367070
Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 7.
1
1, 16, 128, 250, 480, 864, 21600, 62208, 73728
OFFSET
1,2
COMMENTS
There is a finite number of such numbers; we only calculated the terms in [1, 10^10] (Property 1' of Clerc).
LINKS
René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, hal-04507547 [math.nt], 2024. (In French)
EXAMPLE
21600 = 116655_7, (1+1+6+6+5+5)*(1*1*6*6*5*5) = 24*900 = 21600.
MATHEMATICA
Select[Range[7^7], #1 == Times @@ DeleteCases[#2, 0]*Total[#2] & @@ {#, IntegerDigits[#, 7]} &] (* Michael De Vlieger, Mar 25 2024 *)
PROG
(PARI) isok(k, b) = my(d=select(x->(x>0), digits(k, b))); vecprod(d)*vecsum(d) == k;
for (k=1, 10^5, if (isok(k, 7), print1(k, ", ")))
CROSSREFS
KEYWORD
base,nonn,fini,more
AUTHOR
René-Louis Clerc, Jan 10 2024
STATUS
approved