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%I #30 Jul 23 2024 21:24:02
%S 1,4,9,14,25,33,49,60,78,95,121,138,169,189,220,248,289,315,361,390,
%T 434,473,529,564,620,663,720,770,841,885,961,1008,1078,1139,1218,1278,
%U 1369,1425,1508,1580,1681,1743,1849,1914,2010,2093,2209,2280,2394,2475,2584
%N The square of n minus (the largest divisor d of n with 2 <= d <= m-1, or 0 if there is no such divisor).
%F a(n) = n^2 - A032742(n) if n is composite, n^2 otherwise.
%F a(n) = A000290(n) <=> n in { A008578 }.
%e For n = 10, the divisors of n are {1,2,5,10}. The largest nontrivial divisor is 5, so 10 * 10 - 5 = 95.
%t Table[
%t Module[{divisors, largestNonTrivialDivisor},
%t divisors = Divisors[n];
%t largestNonTrivialDivisor = If[Length[divisors] > 2, divisors[[-2]], 0];
%t n^2 - largestNonTrivialDivisor
%t ],
%t {n, 1, 20}
%t ]
%o (Python)
%o def factors(n):
%o return sorted([i for i in range(2, n - 1) if n % i == 0])
%o def main():
%o for i in range(1, 20):
%o fs = factors(i)
%o if len(fs) == 0:
%o l = 0
%o else:
%o l = fs[-1]
%o print(i*i - l)
%o if __name__ == "__main__":
%o main()
%Y Relates to A364391 but uses n^2 instead of n.
%Y Cf. A000040, A000290, A008578, A032742, A160180.
%K nonn
%O 1,2
%A _Stephen Pearson_, Jul 04 2024