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%I #12 May 13 2013 01:50:09
%S 361,551,703,1007,1273,1691,1843,2033,2071,2183,2413,2603,2641,2701,
%T 2831,2923,3071,3173,3293,3743,3781,4033,4313,4351,4541,5143,5263,
%U 5513,6023,6031,6401,6403,6623,6631,6821,7081,7141,7363,7391,7543,8303,8341,8531
%N Numbers not multiples of 9 whose digital sum coincides with digital sum of their largest proper divisor.
%C The number n has a prime factor of the form 18k+1.
%H Antonio Roldán and T. D. Noe, <a href="/A219340/b219340.txt">Table of n, a(n) for n = 1..10000</a> (542 terms from Antonio Roldán)
%e 12673 is in the sequence because 12673 = 19*23*29, their largest proper divisor is 667. Both have a digital sum of 19.
%t Select[Range[2, 10000], Mod[#, 9] > 0 && Total[IntegerDigits[#]] == Total[IntegerDigits[Divisors[#][[-2]]]] &] (* _T. D. Noe_, Nov 20 2012 *)
%o (PARI) largdiv(n)=if(n==1, 1, n/factor(n)[1, 1]) /* _Charles R Greathouse IV_, Jun 15 2011 */
%o digsum(n)={local (d,p); d=0; p=n; while(p,d+=p%10;p=floor(p/10)); return(d)}
%o { k=0; for (n=2, 10^5, if(digsum(n)==digsum(largdiv(n))&&n%9>0, k=k+1;write("B219340.txt",k,", ",n))); } /* Antonio Roldán, Nov 18 2012 */
%K nonn,base
%O 1,1
%A _Antonio Roldán_, Nov 18 2012
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