A138296 - OEIS

%I #5 Jul 20 2016 11:10:34

%S 5,13,7,35,29,5,97,133,13,9,275,641,35,53,8,793,3157,97,351,34,5,2315,

%T 15689,275,2417,152,13,7,6817,78253,793,16839,706,35,29,10,20195,

%U 390881,2315,117713,3368,97,133,58,13,60073,1953637,6817,823671,16354,275,641

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

%C Row k=1 is A109353. Rows k=2,3 and 4 are subsequences of A005063-A005065.

%H 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 T(k,n) = sum_{d in A000040, d| A024619(n)} d^k.

%e Upper left corner of the table starting at row k=1, column n=1:

%e 1|......5.......7.......5.......9.......8.......5.......7.

%e 2|.....13......29......13......53......34......13......29.

%e 3|.....35.....133......35.....351.....152......35.....133.

%e 4|.....97.....641......97....2417.....706......97.....641.

%e 5|....275....3157.....275...16839....3368.....275....3157.

%e 6|....793...15689.....793..117713...16354.....793...15689.

%e 7|...2315...78253....2315..823671...80312....2315...78253.

%e 8|...6817..390881....6817.5765057..397186....6817..390881.

%p A024619 := proc(n)

%p     local a;

%p     if n = 1 then

%p         RETURN(6);

%p     else

%p         for a from A024619(n-1)+1 do

%p             if A001221(a) > 1 then

%p                RETURN(a) ;

%p             fi ;

%p         od:

%p     fi ;

%p end:

%p A138296 := proc(n,j)

%p     local f,beta ;

%p     beta := 0 ;

%p     for f in ifactors( A024619(n) )[2] do

%p         beta := beta+op(1,f)^j ;

%p     od:

%p     RETURN(beta) ;

%p end:

%p 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 easy,nonn,tabl

%O 1,1

%A _R. J. Mathar_, May 07 2008