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A185186
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Numbers divisible by at least one of their digits other than 1.
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3
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2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 20, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 52, 55, 60, 62, 63, 64, 65, 66, 70, 72, 75, 77, 80, 82, 84, 85, 88, 90, 92, 93, 95, 96, 99, 102, 104, 105, 112, 115, 120, 122, 123, 124, 125, 126, 128, 132
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OFFSET
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1,1
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COMMENTS
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The only primes in the sequence are 2, 3, 5, 7. No repunits are eligible.
Also, an interesting class of non-eligible integers consists of some powers of 2, 3 and 7:
"2, 4, 8-less" powers of 2, 2^m = 1, 16, 65536 with m = 0, 4, 16 (a subsequence of A034293);
"3, 9-less" powers of 3, 3^m = {1, 27, 81, 177147, 1162261467}, with m = {0, 3, 4, 11, 19} (a subsequence of A131629);
"seven-less" powers of 7, 7^m, with m = 0, 2, 3, 4, 7, 16, 22, 24, 39 (see 6th row of A136291 Array read by rows: each row is a sequence of numbers k such that n^k does not contain the digit n).
The asymptotic density of numbers having a prime digit is 1 for each prime digit. The asymptotic density of numbers being divisible by 2, 3, 5 or 7 is -Sum_{d|210, d>1}((-1)^omega(d) / d) = 27/35. Also, the asymptotic density of numbers divisible by the first n primes is r(n) where r(1) = 1/2 and r(n) = r(n - 1) + (1 - r(n - 1)) / prime(n). - David A. Corneth, May 28 2017
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LINKS
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MATHEMATICA
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digDivQ[n_] := AnyTrue[IntegerDigits[n], # > 1 && Mod[n, #] == 0 &]; Select[Range[200], digDivQ] (* Giovanni Resta, May 27 2017 *)
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PROG
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(PARI) is(n) = my(d = vecsort(digits(n), , 8), t = 1); while(t<=#d&&d[t] < 2, t++); sum(i=t, #d, n%d[i]==0) > 0 \\ David A. Corneth, May 27 2017
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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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