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Search: id:A138296
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| A138296 |
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Table T(k,n) read along antidiagonals: sum of the kth powers of the distinct prime factors of A024619(n). |
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Row k=1 is A109353. Rows k=2,3 and 4 are subsequences of A005063-A005065.
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LINKS
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J.-M de Koninck, F. Luca, Integers divisible by sums of powers of their prime factors, J. Num. Theory vol 128 (2008) 557-563.
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FORMULA
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T(k,n) = sum_{d in A000040, d| A024619(n)} d^k.
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EXAMPLE
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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.
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MAPLE
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A001221 := proc(n) nops(numtheory[factorset](n)) ; end: 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: T := 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, ", T(n, d-n+1)) ; od: od: # R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 07 2008
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CROSSREFS
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Sequence in context: A094473 A068530 A088315 this_sequence A094474 A064109 A156682
Adjacent sequences: A138293 A138294 A138295 this_sequence A138297 A138298 A138299
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 07 2008
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