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A138296 Table T(k,n) read along antidiagonals: sum of the k-th powers of the distinct prime factors of A024619(n).

%I A138296 #5 Jul 20 2016 11:10:34
%S A138296 5,13,7,35,29,5,97,133,13,9,275,641,35,53,8,793,3157,97,351,34,5,2315,
%T A138296 15689,275,2417,152,13,7,6817,78253,793,16839,706,35,29,10,20195,
%U A138296 390881,2315,117713,3368,97,133,58,13,60073,1953637,6817,823671,16354,275,641
%N A138296 Table T(k,n) read along antidiagonals: sum of the k-th powers of the distinct prime factors of A024619(n).
%C A138296 Row k=1 is A109353. Rows k=2,3 and 4 are subsequences of A005063-A005065.
%H A138296 J.-M de Koninck, F. Luca, <a href="http://dx.doi.org/10.1016/j.jnt.2007.01.010">Integers divisible by sums of powers of their prime factors</a>, J. Num. Theory vol 128 (2008) 557-563.
%F A138296 T(k,n) = sum_{d in A000040, d| A024619(n)} d^k.
%e A138296 Upper left corner of the table starting at row k=1, column n=1:
%e A138296 1|......5.......7.......5.......9.......8.......5.......7.
%e A138296 2|.....13......29......13......53......34......13......29.
%e A138296 3|.....35.....133......35.....351.....152......35.....133.
%e A138296 4|.....97.....641......97....2417.....706......97.....641.
%e A138296 5|....275....3157.....275...16839....3368.....275....3157.
%e A138296 6|....793...15689.....793..117713...16354.....793...15689.
%e A138296 7|...2315...78253....2315..823671...80312....2315...78253.
%e A138296 8|...6817..390881....6817.5765057..397186....6817..390881.
%p A138296 A024619 := proc(n)
%p A138296     local a;
%p A138296     if n = 1 then
%p A138296         RETURN(6);
%p A138296     else
%p A138296         for a from A024619(n-1)+1 do
%p A138296             if A001221(a) > 1 then
%p A138296                RETURN(a) ;
%p A138296             fi ;
%p A138296         od:
%p A138296     fi ;
%p A138296 end:
%p A138296 A138296 := proc(n,j)
%p A138296     local f,beta ;
%p A138296     beta := 0 ;
%p A138296     for f in ifactors( A024619(n) )[2] do
%p A138296         beta := beta+op(1,f)^j ;
%p A138296     od:
%p A138296     RETURN(beta) ;
%p A138296 end:
%p A138296 for d from 1 to 10 do for n from 1 to d do printf("%d,",A138296(n,d-n+1)) ; od: od: # _R. J. Mathar_, May 07 2008
%K A138296 easy,nonn,tabl
%O A138296 1,1
%A A138296 _R. J. Mathar_, May 07 2008