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A378133
Irregular triangle T(n,k) = P(n)*2^k, n >= 0, k = 0..floor(log_2 prime(k+1)), where P = A002110.
2
1, 2, 4, 6, 12, 24, 30, 60, 120, 210, 420, 840, 1680, 2310, 4620, 9240, 18480, 30030, 60060, 120120, 240240, 480480, 510510, 1021020, 2042040, 4084080, 8168160, 9699690, 19399380, 38798760, 77597520, 155195040, 223092870, 446185740, 892371480, 1784742960, 3569485920
OFFSET
0,2
COMMENTS
Subset of A060735.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..3494 (* rows n = 0..349, flattened *)
FORMULA
T(n,k) = A002110(n)*A000079(k), n >= 0, k = 0..A098388(k+1).
T(n,0) = A002110(n).
T(n,1) = A088860(n), n >= 1.
T(n,2) = A102476(n), n >= 2.
T(n,A098388(k+1)) = A378144(n).
Let S(n,j) = A002110(n)*j, n >= 0, j = 0..A006093(n+1) = P(n)*j, n >= 0, j = 0..prime(n+1)-1. Then T(n,k) = S(n, 2^k).
EXAMPLE
Rows n = 0..9:
n\k | 0 1 2 3 4
-------------------------------------------------------------
0 | 1 . . . .
1 | 2 4 . . .
2 | 6 12 24 . .
3 | 30 60 120 . .
4 | 210 420 840 1680 .
5 | 2310 4620 9240 18480 .
6 | 30030 60060 120120 240240 480480
7 | 510510 1021020 2042040 4084080 8168160
8 | 9699690 19399380 38798760 77597520 155195040
9 | 223092870 446185740 892371480 1784742960 3569485920
MATHEMATICA
nn = 16;
MapIndexed[Set[P[First[#2] - 1], #1] &,
FoldList[Times, 1, Prime@ Range[nn + 1] ] ];
Union@ Flatten@
Table[P[i]*2^Range[0, Floor[Log2[Prime[i + 1] ] ] ], {i, 0, nn}]
KEYWORD
nonn,tabf,easy
AUTHOR
Michael De Vlieger, Nov 17 2024
STATUS
approved