A308731 a(n) is the sum of the terms of the symmetric square array defined by M(i,j) = prime(i)+i-j for i >= j and M(i,j) = M(j,i) if i < j.

2, 13, 44, 105, 224, 397, 660, 1001, 1464, 2105, 2866, 3849, 5030, 6373, 7946, 9829, 12048, 14489, 17310, 20459, 23872, 27731, 31972, 36707, 42060, 47861, 54022, 60663, 67688, 75225, 83902, 93147, 103108, 113543, 125014, 136995, 149788, 163419, 177760, 192987, 209126, 225871, 243912, 262595, 282108

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Formula

a(n) = a(n-1) + (2n-1)*prime(n) + n*(n-1). - Charlie Neder, Jun 21 2019

Example

For n=1, the array is 2, and the sum is 2.
.
.                     2  4
For n=2, the array is      and the sum is 13.
.                     4  3
.
.                     2  4  7
For n=3, the array is 4  3  6 and the sum is 44.
                      7  6  5

Prog

(Excel, VBA)
Sub A308731()
n = 50
Cells(1, 1) = 2
p = 0
For i = 2 To n^2
    isPrime = True
    For j = 1 To p - 1
        If i Mod Cells(j, j) = 0 Then
            isPrime = False
            Exit For
        End If
    Next j
    If isPrime then
        p = p + 1
        Cells(p, p) = i
        If p >= n Then
            Exit For
        End If
    End If
Next i
For i = 2 To p
    For j = 1 To i - 1
        Cells(i, j) = Cells(i, i) + i - j
        Cells(j, i) = Cells(i, j)
    Next j
Next i
For i = 1 To n
    Sum = 0
    For k = 1 To i
        For j = 1 To i
            Sum = Sum + Cells(k, j)
            Cells(i, n + 1) = Sum
        Next j
    Next k
Next i
End Sub
(PARI) M(i, j) = if (i>=j, prime(i)+i-j, M(j, i));
a(n) = sum(i=1, n, vecsum(vector(n, k, M(i, k)))); \\ Michel Marcus, Jun 21 2019

Crossrefs

Cf. A000040.

Sequence in context: A102296 A296807 A366310 * A025194 A084156 A002534

Adjacent sequences: A308728 A308729 A308730 * A308732 A308733 A308734

Keyword

nonn

Author

Ali Sada, Jun 20 2019

Extensions

Edited by Michel Marcus, Jun 21 2019

Status

approved