A111948 - OEIS

A111948

Admirable Harshad numbers n such that the subtracted divisor is equal to the digital sum of n.

%I #6 Oct 27 2019 11:12:09

%S 24,42,114,222,402,2022,2202,7588,8596,10014,11202,12102,17668,21102,

%T 27748,29764,31002,32788,39844,42868,43876,45388,46396,48916,49924,

%U 55972,56476,57484,58492,65548,66556,69076,70588,71596,78148,81676

%N Admirable Harshad numbers n such that the subtracted divisor is equal to the digital sum of n.

%H Amiram Eldar, <a href="/A111948/b111948.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2)=42 because 1+2+3+7+14+21-6 = 42 and 42/6 = 7.

%t harsQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && Plus @@ IntegerDigits[n] == ab/2 && ab/2 < n && Divisible[n, ab/2]; Select[Range[100000], harsQ[#] && admQ[#] &] (* _Amiram Eldar_, Oct 27 2019 *)

%Y Cf. A111592, A005349, A111947.

%K base,nonn

%O 1,1

%A _Jason Earls_, Aug 22 2005