A178158 -id:A178158 - cp's OEIS frontend

A292683 Numbers divisible by themselves with first digit removed (A217657), excluding multiples of 10.

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

Offset: 1

M. F. Hasler, Oct 17 2017

Obviously, any term multiplied by 10 would again be a term, so we exclude trailing zeros.
This sequence cannot contain single-digit 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 single-digit 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).

			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.

Harvey P. Dale, Table of n, a(n) for n = 1..712 (All terms up to 10^7.)

Cf. A217657, A178158, A034709.

Cf. A292684, A292685.

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 *)
Select[Range[10,550],Mod[#,10]!=0&&Mod[#,FromDigits[Rest[IntegerDigits[#]]]]==0&] (* Harvey P. Dale, Sep 15 2024 *)

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

A210582 Numbers whose first digit is the remainder of their division by the last digit (in base 10).

Original entry on oeis.org

13, 19, 23, 26, 29, 39, 46, 49, 59, 69, 79, 89, 103, 109, 127, 133, 163, 193, 197, 199, 203, 206, 209, 214, 218, 233, 234, 236, 247, 254, 258, 263, 266, 274, 293, 294, 296, 298, 299, 309, 367, 399, 406, 409, 417, 428, 436, 466, 468, 487, 496, 499, 509, 537, 599, 609, 638, 657, 678, 699, 709, 799, 809, 899

Offset: 1

Eric Angelini and M. F. Hasler, Mar 22 2012

This is a restricted or simplified version of the definition of modest numbers A054986.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
E. Angelini, Not Modest, Mar 22 2012
E. Angelini, Not modest [Cached copy, with permission]

Cf. A054986, A178158.

A subsequence of A067251, disjoint with A034709.

a210582 n = a210582_list !! (n-1)
a210582_list = filter (\x -> mod x (a010879 x) == a000030 x) a067251_list
-- Reinhard Zumkeller, Mar 26 2012

[ n: n in [1..1002] | not IsZero(d[1]) and n mod d[1] eq d[#d] where d is Intseq(n) ];  // Bruno Berselli, Mar 26 2012

is_nm( x )=x%10 && x%(x%10)==x\10^(#Str(x)-1)
for(n=1,999,is_nm(n)&print1(n","))

a(n) mod A010879(a(n)) = A000030(a(n)). [Reinhard Zumkeller, Mar 26 2011]

Edited by M. F. Hasler, Jan 14 2014

A261448 Numbers n >= 100 that are divisible by n mod 100.

Original entry on oeis.org

101, 102, 104, 105, 110, 120, 125, 150, 201, 202, 204, 205, 208, 210, 220, 225, 240, 250, 301, 302, 303, 304, 305, 306, 310, 312, 315, 320, 325, 330, 350, 360, 375, 401, 402, 404, 405, 408, 410, 416, 420, 425, 440, 450, 480, 501, 502, 504, 505, 510, 520, 525, 550

Offset: 1

Giovanni Teofilatto, Aug 19 2015

This sequence can be seen as the union of 99 linear sequences of the form a_i*k+i, for i=1,...,99 and k>0, where a_i depends on i. For example, 100*k+1, 100*k+2, 300*k+3,..., 4700*k+94, 1900*k+95,..., 9900*k+99. Hence, in analogy with A034709, there exist two numbers p and q such that a(p*k+i) = q*k + a(i), where q <= lcm(1,2,...,99). - Giovanni Resta, Aug 20 2015

Cf. A034709, A178158.

Select[Range[100, 1000], Quiet@ Divisible[#, Mod[#, 100]] &] (* Giovanni Resta, Aug 19 2015 *)

isok(n) = (n>100) && (dd = n % 100) && !(n % dd); \\ Michel Marcus, Aug 19 2015

More terms from Michel Marcus, Aug 19 2015

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A292683 Numbers divisible by themselves with first digit removed (A217657), excluding multiples of 10.

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A210582 Numbers whose first digit is the remainder of their division by the last digit (in base 10).

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A261448 Numbers n >= 100 that are divisible by n mod 100.

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