cp's OEIS Frontend

A098034 Numbers that are divisible both by the sum and by the product of the squares of their digits.

%I A098034 #19 Nov 16 2013 10:12:53
%S A098034 111,11112,1122112,111111111,122121216,1111112112,1111211136,
%T A098034 1116122112,1211162112,11111113116,11111121216,11112122112,
%U A098034 11121114112,11132111232,11133122112,11213111232,11311322112,12111213312,21111311232,31111221312
%N A098034 Numbers that are divisible both by the sum and by the product of the squares of their digits.
%C A098034 Also called "uncommon numbers". Sequence contains the repunits R_m, where m=A014950,m>1. - _Lekraj Beedassy_, Jul 14 2008
%C A098034 Called "insolite numbers" in the paper by J.-M. De Koninck and N. Doyon, which contains a list of insolite numbers below 10^18. Their list lacks a(63)=112264112111616. They conjectured that 1111111111131111131111111111175 is the smallest insolite number containing the digit '5'. I verified this claim and found a further such number, 1111111111111111117111111111911111375, which may not be the second one. - _Giovanni Resta_, Oct 19 2012
%D A098034 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 111, p. 39, Ellipses, Paris 2008.
%H A098034 Lekraj Beedassy and Giovanni Resta, <a href="/A098034/b098034.txt">Table of n, a(n) for n = 1..428</a> (terms < 10^20, first 39 terms from Lekraj Beedassy)
%H A098034 J.-M. De Koninck and N. Doyon, <a href="http://www.jeanmariedekoninck.mat.ulaval.ca/fileadmin/jmdk/Documents/Publications/2001_on_a_very_thin_sequence_of_integers.pdf"> On a very thin sequence of integers</a>, Annales Rolando Eötvös Nominatae, 20:157-177 (2001)
%e A098034 1122112 is in the sequence because 1^2 + 1^2 + 2^2 + 2^2 + 1^2 + 1^2 + 2^2=16,(1*1*2*2*1*1*2)^2=64 and we have 1122112=16*70132=64*17533.
%K A098034 nonn,base
%O A098034 1,1
%A A098034 _Lekraj Beedassy_, Sep 10 2004
%E A098034 More terms from _Lekraj Beedassy_, Jul 14 2008
%E A098034 Missing term a(11) inserted, b-file corrected and extended to terms < 10^20 by _Giovanni Resta_, Oct 19 2012