A368582 a(n) = floor((sigma(n) + 1) / 2).

1, 2, 2, 4, 3, 6, 4, 8, 7, 9, 6, 14, 7, 12, 12, 16, 9, 20, 10, 21, 16, 18, 12, 30, 16, 21, 20, 28, 15, 36, 16, 32, 24, 27, 24, 46, 19, 30, 28, 45, 21, 48, 22, 42, 39, 36, 24, 62, 29, 47, 36, 49, 27, 60, 36, 60, 40, 45, 30, 84, 31, 48, 52, 64, 42, 72, 34, 63

Offset: 1

Author

Peter Luschny, Dec 31 2023

Keywords

• nonn

Crossrefs

Cf. A000203, A000079 (2^n), A000396 (perfect), A088580, A317306, A368207 (Bacher).

Programs

Julia

using Nemo
A368582(n::Int) = div(divisor_sigma(n, 1) + 1, 2)
println([A368582(n) for n in 1:68])

Mathematica

Array[Floor[(DivisorSigma[1, #] + 1)/2] &, 120] (* Michael De Vlieger, Dec 31 2023 *)

PARI

a(n) = (sigma(n)+1)\2; \\ Michel Marcus, Jan 03 2024

Formula

a(p) = (p + 1) / 2 for all odd prime p.

a(n) = n <=> n term of union of A000079 and A000396. (If there are no odd perfect numbers also of A317306).

a(n) = floor(A088580(n)/2). - Omar E. Pol, Dec 31 2023