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A367070
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Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 7.
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1
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OFFSET
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1,2
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COMMENTS
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There is a finite number of such numbers; we only calculated the terms in [1, 10^10] (Property 1' of Clerc).
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LINKS
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EXAMPLE
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21600 = 116655_7, (1+1+6+6+5+5)*(1*1*6*6*5*5) = 24*900 = 21600.
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MATHEMATICA
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Select[Range[7^7], #1 == Times @@ DeleteCases[#2, 0]*Total[#2] & @@ {#, IntegerDigits[#, 7]} &] (* Michael De Vlieger, Mar 25 2024 *)
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PROG
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(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, ", ")))
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CROSSREFS
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KEYWORD
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base,nonn,fini,more
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AUTHOR
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STATUS
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approved
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