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Non-Niven (or non-Harshad) numbers: numbers which are not a multiple of the sum of their digits.
9

%I #16 Jun 17 2018 02:44:50

%S 11,13,14,15,16,17,19,22,23,25,26,28,29,31,32,33,34,35,37,38,39,41,43,

%T 44,46,47,49,51,52,53,55,56,57,58,59,61,62,64,65,66,67,68,69,71,73,74,

%U 75,76,77,78,79,82,83,85,86,87,88,89,91,92,93,94,95,96,97,98,99,101

%N Non-Niven (or non-Harshad) numbers: numbers which are not a multiple of the sum of their digits.

%C A188641(a(n)) = 0; A070635(a(n)) > 0. [_Reinhard Zumkeller_, Apr 07 2011]

%H Harry J. Smith, <a href="/A065877/b065877.txt">Table of n, a(n) for n = 1..1000</a>

%e 13 is in the list because 13 is not a multiple of 1 + 3 = 4.

%t Select[Range[101],!IntegerQ[#/Total[IntegerDigits[#]]] &] (* _Jayanta Basu_, May 05 2013 *)

%o (PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) } { n=0; for (m=1, 10^9, if (m%SumD(m), write("b065877.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Nov 03 2009

%o (Haskell)

%o import Data.List (findIndices)

%o a065877 n = a065877_list !! (n-1)

%o a065877_list = map succ $ findIndices (> 0) $ map a070635 [1..]

%o -- _Reinhard Zumkeller_, Apr 07 2011

%Y Complement of A005349. Cf. A003635, A007953, A065878.

%Y Cf. A188643.

%K base,nonn

%O 1,1

%A _Henry Bottomley_, Nov 26 2001