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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,...), ... 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 15:55 EDT 2020. Contains 337443 sequences. (Running on oeis4.)