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A342445
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Numbers that are divisible by their nonzero digits but are not divisible by the product of their nonzero digits.
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0
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22, 33, 44, 48, 55, 66, 77, 88, 99, 122, 124, 126, 155, 162, 168, 184, 202, 204, 222, 244, 248, 264, 280, 288, 303, 324, 330, 333, 336, 366, 396, 404, 408, 412, 420, 424, 440, 444, 448, 488, 505, 515, 555, 606, 636, 648, 660, 666, 707, 728, 770, 777, 784, 808, 824, 840
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OFFSET
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1,1
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COMMENTS
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Numbers that are divisible by the product of their nonzero digits (A055471) are trivially divisible by each of their nonzero digits (A002796), but the converse is false. This sequence = A002796 \ A055471 and consists of these counterexamples.
This sequence differs from A337163: the first sixteen terms are the same but a(17) = 202 while A337163(17) = 222.
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LINKS
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EXAMPLE
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204 is divisible by 2 and 4 but 204 is not divisible by 2*4 = 8, hence 204 is a term.
248 is divisible by 2, by 4 and by 8 but 248 is not divisible by 2*4*8 = 64, hence 248 is a term.
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MATHEMATICA
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q[n_] := AllTrue[(d = Select[IntegerDigits[n], # > 0 &]), Divisible[n, #] &] && ! Divisible[n, Times @@ d]; Select[Range[840], q] (* Amiram Eldar, Mar 21 2021 *)
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PROG
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(PARI) isok(m) = my(d=select(x->(x != 0), digits(m))); (m % vecprod(d)) && (sum(k=1, #d, m % d[k]) == 0); \\ Michel Marcus, Mar 22 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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STATUS
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approved
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