A368582 - OEIS

%I #17 Jan 03 2024 05:35:50

%S 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,

%T 28,15,36,16,32,24,27,24,46,19,30,28,45,21,48,22,42,39,36,24,62,29,47,

%U 36,49,27,60,36,60,40,45,30,84,31,48,52,64,42,72,34,63

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

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

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

%F a(n) = floor(A088580(n)/2). - _Omar E. Pol_, Dec 31 2023

%t Array[Floor[(DivisorSigma[1, #] + 1)/2] &, 120] (* _Michael De Vlieger_, Dec 31 2023 *)

%o (Julia)

%o using Nemo

%o A368582(n::Int) = div(divisor_sigma(n, 1) + 1, 2)

%o println([A368582(n) for n in 1:68])

%o (PARI) a(n) = (sigma(n)+1)\2; \\ _Michel Marcus_, Jan 03 2024

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

%K nonn

%O 1,2

%A _Peter Luschny_, Dec 31 2023