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A319012
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a(n) = Sum_{i=1..n} prime(n*(i - 1) + i).
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1
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2, 9, 36, 99, 224, 407, 724, 1129, 1700, 2451, 3382, 4543, 5986, 7661, 9724, 12041, 14762, 17891, 21482, 25499, 29998, 35083, 40644, 46873, 53620, 61077, 69240, 78119, 87686, 98053, 109290, 121503, 134388, 148297, 162970, 178905, 195770, 213725, 232794
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OFFSET
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1,1
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COMMENTS
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a(n) is the trace of the n X n matrix M(n) whose first row contains the first n primes in increasing order, the second row of M(n) contains the next n primes in increasing order, and so on (see examples below).
Conjecture: a(2) and a(3) are the only terms that are perfect squares.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} A000040(n*(i - 1) + i).
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EXAMPLE
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For n = 1 the matrix M(1) is
2
with trace Tr(M(1)) = a(1) = 2.
For n = 2 the matrix M(2) is
2, 3
5, 7
with Tr(M(2)) = a(2) = 9.
For n = 3 the matrix M(3) is
2, 3, 5
7, 11, 13
17, 19, 23
with Tr(M(3)) = a(3) = 36.
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MAPLE
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a:=n->add(ithprime(n*(i-1)+i), i=1..n): seq(a(n), n=1..40); # Muniru A Asiru, Sep 17 2018
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MATHEMATICA
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Table[Tr[Partition[Array[Prime, n^2], n]], {n, 40}]
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PROG
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(PARI) a(n) = sum(i=1, n, prime(n*(i - 1) + i)); \\ Michel Marcus, Sep 07 2018
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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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