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

5, 13, 7, 35, 29, 5, 97, 133, 13, 9, 275, 641, 35, 53, 8, 793, 3157, 97, 351, 34, 5, 2315, 15689, 275, 2417, 152, 13, 7, 6817, 78253, 793, 16839, 706, 35, 29, 10, 20195, 390881, 2315, 117713, 3368, 97, 133, 58, 13, 60073, 1953637, 6817, 823671, 16354, 275, 641

Offset: 1

Author

R. J. Mathar, May 07 2008

Keywords

• easy
• nonn
• tabl

Comments

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

Examples

			Upper left corner of the table starting at row k=1, column n=1:
1|......5.......7.......5.......9.......8.......5.......7.
2|.....13......29......13......53......34......13......29.
3|.....35.....133......35.....351.....152......35.....133.
4|.....97.....641......97....2417.....706......97.....641.
5|....275....3157.....275...16839....3368.....275....3157.
6|....793...15689.....793..117713...16354.....793...15689.
7|...2315...78253....2315..823671...80312....2315...78253.
8|...6817..390881....6817.5765057..397186....6817..390881.
		

Links

• J.-M de Koninck, F. Luca, Integers divisible by sums of powers of their prime factors, J. Num. Theory vol 128 (2008) 557-563.

Programs

Maple

A024619 := proc(n)
    local a;
    if n = 1 then
        RETURN(6);
    else
        for a from A024619(n-1)+1 do
            if A001221(a) > 1 then
               RETURN(a) ;
            fi ;
        od:
    fi ;
end:
A138296 := proc(n,j)
    local f,beta ;
    beta := 0 ;
    for f in ifactors( A024619(n) )[2] do
        beta := beta+op(1,f)^j ;
    od:
    RETURN(beta) ;
end:
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

Formula

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