A238760 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,...), ...
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
Offset: 1
Keywords
Examples
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 ........................................................ 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. .............................................
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Maple
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: -
Mathematica
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 *) -
Sage
def a(n): return sum([nth_prime((k+1)*(k+2)/2+n-k) for k in range(floor(n/2),n+1)]) # Ralf Stephan, Mar 09 2014
Formula
a(n) = sum(k=floor(n/2)...n+1, A000040(n+(k+1)*(k+2)/2-k) ). - Ralf Stephan, Mar 09 2014