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A082771
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Triangular array, read by rows: t(n,k) = Sum(d^k: d|n), 0<=k<n.
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3
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1, 2, 3, 2, 4, 10, 3, 7, 21, 73, 2, 6, 26, 126, 626, 4, 12, 50, 252, 1394, 8052, 2, 8, 50, 344, 2402, 16808, 117650, 4, 15, 85, 585, 4369, 33825, 266305, 2113665, 3, 13, 91, 757, 6643, 59293, 532171, 4785157, 43053283, 4, 18, 130, 1134, 10642, 103158, 1015690
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| t(n,0)=A000005(n); t(n,1)=A000203(n), n>1; t(n,2)=A001157(n), n>2; t(n,3)=A001158(n), n>3; t(n,4)=A001159(n), n>4; t(n,5)=A001160(n), n>5; t(n,6)=A013954(n), n>6;
t(n,n)=A023887(n).
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LINKS
| T. D. Noe, Rows n=1..100, flattened
Eric Weisstein's World of Mathematics, Divisor Function
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FORMULA
| t(n, k) = Product(((p^((e(n, p)+1)*k))-1)/(p^k-1): n=Product(p^e(n, p): p prime)), 0<=k<n.
t(2,k)=A000051(k); t(3,k)=A034472(k); t(4,k)=A001576(k); t(5,k)=A034474(k); t(6,k)=A034488(k); t(7,k)=A034491(k); t(8,k)=A034496(k); t(9,k)=A034513(k); t(10,k)=A034517(k); t(11,k)=A034524(k); t(12,k)=A034660(k). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 29 2006
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EXAMPLE
| Comment from R. J. Mathar: The triangle may be extended to a rectangular array:
1 1 1 1 1 1 1 1 1 1 1 ...
2 3 5 9 17 33 65 129 257 513 1025 ...
2 4 10 28 82 244 730 2188 6562 19684 59050 ...
3 7 21 73 273 1057 4161 16513 65793 262657 1049601 ...
2 6 26 126 626 3126 15626 78126 390626 1953126 9765626 ...
4 12 50 252 1394 8052 47450 282252 1686434 10097892 60526250 ...
2 8 50 344 2402 16808 117650 823544 5764802 40353608 282475250 ...
4 15 85 585 4369 33825 266305 2113665 16843009 134480385 1074791425 ...
3 13 91 757 6643 59293 532171 4785157 43053283 387440173 3486843451 ...
4 18 130 1134 10642 103158 1015690 10078254 100390882 1001953638...
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CROSSREFS
| Cf. A000005, A000203, A001157, A001158, A001159, A001160.
Cf. A013954, A013955, A013956, A013957, A013958, A013959, A013960, A013961, A013962, A013963.
Cf. A013964, A013965, A013966, A013967, A013968, A013969, A013970, A013971, A013972.
Sequence in context: A154578 A059576 A034800 * A127157 A202714 A022662
Adjacent sequences: A082768 A082769 A082770 * A082772 A082773 A082774
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 21 2003
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EXTENSIONS
| Corrected by R. J. Mathar, Dec 05 2006
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