

A292683


Numbers divisible by themselves with first digit removed (A217657), excluding multiples of 10.


2



11, 12, 15, 21, 22, 24, 25, 31, 32, 33, 35, 36, 41, 42, 44, 45, 48, 51, 52, 55, 61, 62, 63, 64, 65, 66, 71, 72, 75, 77, 81, 82, 84, 85, 88, 91, 92, 93, 95, 96, 99, 101, 102, 104, 105, 125, 201, 202, 204, 205, 208, 225, 301, 302, 303, 304, 305, 306, 312, 315, 325, 375, 401, 402, 404, 405, 408, 416, 425, 501
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OFFSET

1,1


COMMENTS

Obviously, any term multiplied by 10 would again be a term, so we exclude trailing zeros.
This sequence cannot contain singledigit numbers (which would yield 0 with the initial digit removed), in contrast to A178158 (numbers divisible by every suffix of n) where the condition is vacuously satisfied for singledigit numbers.
416 is the first term in the present sequence which is not in A178158.
See A292684 and A292685 for the (number of) multiples of N = a(n) which have the same property and yield the same ratio N/A217657(N).


LINKS

Table of n, a(n) for n=1..70.


EXAMPLE

12 is in the sequence because it is divisible by 2.
416 is in the sequence because it is divisible by 16, 416 = 4*4*25 + 16.


MATHEMATICA

fQ[n_] := Mod[n, 10] > 0 && Mod[n, n  Quotient[n, 10^Floor@ Log10@ n] 10^Floor@ Log10@ n] == 0; Select[ Range[11, 501], fQ] (* Robert G. Wilson v, Oct 18 2017 *)


PROG

(PARI) select( is(n)=n%10&&(m=n%10^logint(n, 10))&&!(n%m), [0..500])


CROSSREFS

Cf. A217657, A178158, A034709.
Cf. A292684, A292685.
Sequence in context: A213309 A128997 A189836 * A139138 A249766 A113600
Adjacent sequences: A292680 A292681 A292682 * A292684 A292685 A292686


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Oct 17 2017


STATUS

approved



