cp's OEIS Frontend

A087142 Numbers divisible by their individual digits, but not by the sum of their digits (counted with multiplicity).

%I A087142 #20 Aug 24 2024 20:21:20
%S A087142 11,15,22,33,44,55,66,77,88,99,115,122,124,128,155,168,175,184,212,
%T A087142 244,248,366,384,412,424,488,515,636,672,728,784,816,824,848,1111,
%U A087142 1112,1113,1115,1124,1131,1144,1155,1176,1184,1197,1222,1244,1248,1266,1288,1311
%N A087142 Numbers divisible by their individual digits, but not by the sum of their digits (counted with multiplicity).
%C A087142 Intersection of A034838 and A065877.
%H A087142 David A. Corneth, <a href="/A087142/b087142.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)
%e A087142 488 is in the sequence as its divisible by its individual digits but not by the sum of its digits counted with multiplicity. That is 488 is divisible by 4 and 8 but not by 4 + 8 + 8 = 20. - _David A. Corneth_, Jan 28 2021
%t A087142 didQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&AllTrue[n/idn, IntegerQ] && !Divisible[n,Total[idn]]]; Select[Range[1300], didQ] (* The program uses the AllTrue function from Mathematica version 10 *)  (* _Harvey P. Dale_, Apr 18 2016 *)
%o A087142 (PARI) is(n) = { my(d = digits(n), sd = vecsum(d), s = Set(d)); if(n == 0 || s[1] == 0, return(0)); if(n % sd != 0, for(i = 1, #s, if(n % s[i] != 0, return(0) ) ); return(1) ); 0 } \\ _David A. Corneth_, Jan 28 2021
%o A087142 (Python)
%o A087142 def ok(n):
%o A087142     d = list(map(int, str(n)))
%o A087142     return 0 not in d and n%sum(d) and all(n%di == 0 for di in set(d))
%o A087142 print([k for k in range(1312) if ok(k)]) # _Michael S. Branicky_, Nov 15 2021
%Y A087142 Cf. A034838, A052382, A065877, A087141.
%Y A087142 Cf. A337163 (similar, with product).
%K A087142 nonn,base
%O A087142 1,1
%A A087142 _Reinhard Zumkeller_, Aug 18 2003