This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A292683 #27 Jul 31 2025 06:59:13 %S A292683 11,12,15,21,22,24,25,31,32,33,35,36,41,42,44,45,48,51,52,55,61,62,63, %T A292683 64,65,66,71,72,75,77,81,82,84,85,88,91,92,93,95,96,99,101,102,104, %U A292683 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 %N A292683 Numbers divisible by themselves with first digit removed (A217657), excluding multiples of 10. %C A292683 Obviously, any term multiplied by 10 would again be a term, so we exclude trailing zeros. %C A292683 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. %C A292683 416 is the first term in the present sequence which is not in A178158. %C A292683 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). %H A292683 Harvey P. Dale, <a href="/A292683/b292683.txt">Table of n, a(n) for n = 1..712</a> (All terms up to 10^7.) %e A292683 12 is in the sequence because it is divisible by 2. %e A292683 416 is in the sequence because it is divisible by 16, 416 = 4*4*25 + 16. %t A292683 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 *) %t A292683 Select[Range[10,550],Mod[#,10]!=0&&Mod[#,FromDigits[Rest[IntegerDigits[#]]]]==0&] (* _Harvey P. Dale_, Sep 15 2024 *) %o A292683 (PARI) select( is(n)=n%10&&(m=n%10^logint(n,10))&&!(n%m), [0..500]) %Y A292683 Cf. A217657, A178158, A034709. %Y A292683 Cf. A292684, A292685. %K A292683 nonn,base %O A292683 1,1 %A A292683 _M. F. Hasler_, Oct 17 2017