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A185186 Numbers divisible by at least one of their digits other than 1.

%I A185186 #46 Aug 30 2020 10:13:26
%S A185186 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,
%T A185186 45,48,50,52,55,60,62,63,64,65,66,70,72,75,77,80,82,84,85,88,90,92,93,
%U A185186 95,96,99,102,104,105,112,115,120,122,123,124,125,126,128,132
%N A185186 Numbers divisible by at least one of their digits other than 1.
%C A185186 The only primes in the sequence are 2, 3, 5, 7. No repunits are eligible.
%C A185186 Also, an interesting class of non-eligible integers consists of some powers of 2, 3 and 7:
%C A185186 "2, 4, 8-less" powers of 2, 2^m = 1, 16, 65536 with m = 0, 4, 16 (a subsequence of A034293);
%C A185186 "3, 9-less" powers of 3, 3^m = {1, 27, 81, 177147, 1162261467}, with m = {0, 3, 4, 11, 19} (a subsequence of A131629);
%C A185186 "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).
%C A185186 Asymptotic density 27/35 = 0.771... - _Charles R Greathouse IV_, Mar 11 2011
%C A185186 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
%H A185186 Giovanni Resta, <a href="/A185186/b185186.txt">Table of n, a(n) for n = 1..10000</a>
%t A185186 digDivQ[n_] := AnyTrue[IntegerDigits[n], # > 1 && Mod[n, #] == 0 &]; Select[Range[200], digDivQ] (* _Giovanni Resta_, May 27 2017 *)
%o A185186 (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
%Y A185186 Cf. A187398, A187516, A187238, A187533, A187534, A187551.
%K A185186 nonn,base
%O A185186 1,1
%A A185186 _Zak Seidov_, Mar 11 2011
%E A185186 Name edited by _Alonso del Arte_, May 16 2017