A297792 a(n) = Sum_{d|n} min(d, n/d)^2.

1, 2, 2, 6, 2, 10, 2, 10, 11, 10, 2, 28, 2, 10, 20, 26, 2, 28, 2, 42, 20, 10, 2, 60, 27, 10, 20, 42, 2, 78, 2, 42, 20, 10, 52, 96, 2, 10, 20, 92, 2, 100, 2, 42, 70, 10, 2, 132, 51, 60, 20, 42, 2, 100, 52, 140, 20, 10, 2, 182, 2, 10, 118, 106, 52, 100, 2, 42, 20

Offset: 1

Author

Seiichi Manyama, Jan 06 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Sum_{d|n} min(d, n/d)^k: A117004 (k=1), this sequence (k=2), A297793 (k=3), A297794 (k=4), A297795 (k=5).

Programs

Mathematica

a[n_] := Block[{d = Divisors@n}, Plus @@ (Min[#, n/#]^2 & /@ d)]; Array[a, 70] (* Robert G. Wilson v, Jan 06 2018 *)

PARI

{a(n) = sumdiv(n, d, min(d, n/d)^2)}

Formula

From Michel Marcus, Jan 09 2018: (Start)

a(p) = 2, for prime p.

a(2p) = 10, for odd prime p. (End)

a(r*p) = 2 + 2*r^2, where r, p are primes and p > r. - Bruno Berselli, Jan 09 2018