OFFSET
1,1
COMMENTS
a(n) is an upper bound for A180128(n).
LINKS
Ortwin Gasper, Hugo Pfoertner and Markus Sigg, An Upper Bound for the Determinant of a Matrix with given Entry Sum and Square Sum JIPAM, Vol. 10, Iss. 3, Art. 63, 2008
Markus Sigg, Gasper's determinant theorem, revisited, arXiv:1804.02897 [math.CO], 2018.
FORMULA
Let c = A007504(n^2)/n [(1/n)*sum of first n^2 primes]
and d = A024450(n^2)/n [(1/n)*sum of first n^2 squares of primes]
Then a(n) = floor(c*sqrt((d-t)^(n-1))) with t = (c^2-d)/(n-1).
log(a(n)) ~ (5*log(n) - log(3))*n/2 + n*log(log(n)). - Vaclav Kotesovec, Aug 28 2021
PROG
(PARI) a180127(n)={if(n<2, 2, my(c=sum(k=1, n^2, prime(k))/n, d=sum(k=1, n^2, prime(k)^2)/n, t=(c^2-d)/(n-1)); floor(c*sqrt((d-t)^(n-1))))} \\ Hugo Pfoertner, Aug 27 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Aug 12 2010
STATUS
approved