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).

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

Links

Table of n, a(n) for n=1..51.

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.

Cf. A000040, A000290, A008578, A032742, A160180.

Sequence in context: A004630 A073497 A244941 * A086192 A105503 A095169

Adjacent sequences: A372812 A372813 A372814 * A372816 A372817 A372818

Keyword

nonn

Author

Stephen Pearson, Jul 04 2024

Status

approved