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

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = sum(k=floor(n/2)...n+1, A000040(n+(k+1)*(k+2)/2-k) ). - Ralf Stephan, Mar 09 2014

Example

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.
.............................................

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 *)

Prog

(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

Crossrefs

Cf. A000040, A064694.

Sequence in context: A305050 A279898 A221066 * A174477 A024997 A081157

Adjacent sequences: A238757 A238758 A238759 * A238761 A238762 A238763

Keyword

nonn

Author

Michel Lagneau, Mar 05 2014

Status

approved