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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
OFFSET
1,1
COMMENTS
Row k=1 is A109353. Rows k=2,3 and 4 are subsequences of A005063-A005065.
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.
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: A068530 A340802 A088315 * A094474 A064109 A175484
KEYWORD
easy,nonn,tabl
AUTHOR
R. J. Mathar, May 07 2008
STATUS
approved