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A238760
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Sum of column entries of the table with rows of prime numbers (2,3,0,0,...), (0,5,7,11,0,...), (0,0,13,17,19,23,0,...), (0,0,0,29,31,37,41,43,0,...), ...
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1
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2, 8, 20, 57, 97, 186, 286, 447, 623, 914, 1190, 1633, 2021, 2642, 3196, 3997, 4745, 5830, 6792, 8149, 9345, 11040, 12502, 14559, 16323, 18766, 20894, 23837, 26313, 29712, 32608, 36539, 39885, 44364, 48118, 53227, 57557, 63322, 68136, 74585, 80017, 87168
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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2 3
0 5 7 11
0 0 13 17 19 23
0 0 0 29 31 37 41 43
0 0 0 0 47 53 59 61 67 71
0 0 0 0 0 73 79 83 89 97 101 103
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sum of the first column = 2.
sum of the second column = 3 + 5 = 8.
sum of the third column = 7 + 13 = 20.
sum of the fourth column = 11 + 17 + 29 = 57.
sum of the fifth column = 19 + 31 + 47 = 97.
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MAPLE
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with(numtheory):nn:=50:mm:=500:T:=array(1..nn, 1..mm):for i from 1 to nn do:for j from 1 to mm do:T[i, j]:=0:od:od:m:=0:for n from 1 to nn do: for k from n to 2*n do: m:=m+1:T[n, k]:=ithprime(m):od:od:for p from 1 to nn do : s:=sum('T[q, p]', 'q'=1..nn): printf(`%d, `, s):od:
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MATHEMATICA
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With[{nn=50}, PadRight[#, nn]&/@(Join[Table[0, Length[#]-2], #]&/@ TakeList[ Prime[Range[((nn-1)(2+nn))/2]], Range[2, nn]])]//Total (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Feb 16 2018 *)
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PROG
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(Sage)
def a(n):
return sum([nth_prime((k+1)*(k+2)/2+n-k) for k in range(floor(n/2), n+1)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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