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

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

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Last modified June 16 15:17 EDT 2019. Contains 324152 sequences. (Running on oeis4.)