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

11, 15, 22, 33, 44, 55, 66, 77, 88, 99, 115, 122, 124, 128, 155, 168, 175, 184, 212, 244, 248, 366, 384, 412, 424, 488, 515, 636, 672, 728, 784, 816, 824, 848, 1111, 1112, 1113, 1115, 1124, 1131, 1144, 1155, 1176, 1184, 1197, 1222, 1244, 1248, 1266, 1288, 1311

Offset

1,1

Comments

Intersection of A034838 and A065877.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Example

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

Mathematica

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 *)087142"]

Prog

(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
(Python)
def ok(n):
    d = list(map(int, str(n)))
    return 0 not in d and n%sum(d) and all(n%di == 0 for di in set(d))
print([k for k in range(1312) if ok(k)]) # Michael S. Branicky, Nov 15 2021

Crossrefs

Cf. A034838, A052382, A065877, A087141.

Cf. A337163 (similar, with product).

Sequence in context: A104628 A045564 A285271 * A158019 A228205 A343416

Adjacent sequences: A087139 A087140 A087141 * A087143 A087144 A087145

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 18 2003

Status

approved