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A372815
The square of n minus (the largest divisor d of n with 2 <= d <= m-1, or 0 if there is no such divisor).
0
1, 4, 9, 14, 25, 33, 49, 60, 78, 95, 121, 138, 169, 189, 220, 248, 289, 315, 361, 390, 434, 473, 529, 564, 620, 663, 720, 770, 841, 885, 961, 1008, 1078, 1139, 1218, 1278, 1369, 1425, 1508, 1580, 1681, 1743, 1849, 1914, 2010, 2093, 2209, 2280, 2394, 2475, 2584
OFFSET
1,2
FORMULA
a(n) = n^2 - A032742(n) if n is composite, n^2 otherwise.
a(n) = A000290(n) <=> n in { A008578 }.
EXAMPLE
For n = 10, the divisors of n are {1,2,5,10}. The largest nontrivial divisor is 5, so 10 * 10 - 5 = 95.
MATHEMATICA
Table[
Module[{divisors, largestNonTrivialDivisor},
divisors = Divisors[n];
largestNonTrivialDivisor = If[Length[divisors] > 2, divisors[[-2]], 0];
n^2 - largestNonTrivialDivisor
],
{n, 1, 20}
]
PROG
(Python)
def factors(n):
return sorted([i for i in range(2, n - 1) if n % i == 0])
def main():
for i in range(1, 20):
fs = factors(i)
if len(fs) == 0:
l = 0
else:
l = fs[-1]
print(i*i - l)
if __name__ == "__main__":
main()
CROSSREFS
Relates to A364391 but uses n^2 instead of n.
Sequence in context: A004630 A073497 A244941 * A086192 A105503 A095169
KEYWORD
nonn
AUTHOR
Stephen Pearson, Jul 04 2024
STATUS
approved