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A337163
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Numbers divisible by their individual digits, but not by the product of their digits.
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3
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22, 33, 44, 48, 55, 66, 77, 88, 99, 122, 124, 126, 155, 162, 168, 184, 222, 244, 248, 264, 288, 324, 333, 336, 366, 396, 412, 424, 444, 448, 488, 515, 555, 636, 648, 666, 728, 777, 784, 824, 848, 864, 888, 936, 999, 1122, 1124, 1128, 1144, 1155, 1164, 1222
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OFFSET
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1,1
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COMMENTS
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The sequence is infinite. For example, all numbers of the form ((10^n-1)/9)*(10^2)+24 are terms for n > 0. The numbers of this form will never be divisible by 8 but they will always be divisible by 1, 2 and 4. Also there are infinitely many terms any three of whose consecutive digits are distinct, for example, concatenations of 124. Are there infinitely many terms which don't consist of periodically repeating substrings? - Metin Sariyar, Jan 28 2021
Every repdigit non-repunit with at least 2 digits is a term. - Bernard Schott, Jan 28 2021
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LINKS
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EXAMPLE
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48 is divisible by 4 and 8, but 48 is not divisible by 4*8 = 32, so 48 is a term.
128 is divisible by 1, 2 and 8, and 128 is divisible by 1*2*8 = 16 with 128 = 16*8, so 128 is not a term.
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MATHEMATICA
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q[n_] := AllTrue[(digits = IntegerDigits[n]), # > 0 && Divisible[n, #] &] && !Divisible[n, Times @@ digits]; Select[Range[1000], q] (* Amiram Eldar, Jan 28 2021 *)
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PROG
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(PARI) isok(n) = my(d=digits(n)); if (vecmin(d), for (i=1, #d, if (n % d[i], return(0))); (n % vecprod(d))); \\ Michel Marcus, Jan 28 2021
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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