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

1,1

Comments

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).

Links

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

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 *)
Select[Range10, 550], Mod[#, 10]!=0&&Mod[#, FromDigits[Rest[IntegerDigits[#]]]]==0&] (* Harvey P. Dale, Sep 15 2024 *)

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