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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). 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..52.

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

FORMULA

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

EXAMPLE

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.

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

CROSSREFS

Sequence in context: A094473 A068530 A088315 * A094474 A064109 A175484

Adjacent sequences:  A138293 A138294 A138295 * A138297 A138298 A138299

KEYWORD

easy,nonn,tabl

AUTHOR

R. J. Mathar, May 07 2008

STATUS

approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)