

A185186


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


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The only primes in the sequence are 2, 3, 5, 7. No repunits are eligible.
Also, an interesting class of noneligible integers consists of some powers of 2, 3 and 7:
"2, 4, 8less" powers of 2, 2^m = 1, 16, 65536 with m = 0, 4, 16 (a subsequence of A034293);
"3, 9less" powers of 3, 3^m = {1, 27, 81, 177147, 1162261467}, with m = {0, 3, 4, 11, 19} (a subsequence of A131629);
"sevenless" 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).
Asymptotic density 27/35 = 0.771...  Charles R Greathouse IV, Mar 11 2011
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_{d210, 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


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000


MATHEMATICA

digDivQ[n_] := AnyTrue[IntegerDigits[n], # > 1 && Mod[n, #] == 0 &]; Select[Range[200], digDivQ] (* Giovanni Resta, May 27 2017 *)


PROG

(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


CROSSREFS

Cf. A187398, A187516, A187238, A187533, A187534, A187551.
Sequence in context: A008816 A002271 A048381 * A336580 A115569 A064653
Adjacent sequences: A185183 A185184 A185185 * A185187 A185188 A185189


KEYWORD

nonn,base


AUTHOR

Zak Seidov, Mar 11 2011


EXTENSIONS

Name edited by Alonso del Arte, May 16 2017


STATUS

approved



