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).
A d-digit number k is a term if and only if k = a*10^(d-1) + b where 1<= a <= 9, b < 10^(d-1) is a divisor of a*10^(d-1) and is not divisible by 10. - Robert Israel, Sep 16 2025
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1 .. 712 from Harvey P. Dale)
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.
MAPLE
f:= proc(d) local R, a, n;
R:= NULL:
for a from 1 to 9 do
R:= R, op(sort(map(t -> t + a*10^(d-1), select(t -> t mod 10 <> 0 and t < 10^(d-1), convert(numtheory:-divisors(a*10^(d-1)), list)))))
od;
R
end proc:
seq(f(d), d=2..4); # Robert Israel, Sep 16 2025
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[Range[10, 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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Oct 17 2017
STATUS
approved