A363735 - OEIS

%I #22 Aug 06 2023 17:51:08

%S 1,2,4,8,11,22,22,44,44,66,74,112,90,158,158,184,197,274,240,344,306,

%T 382,422,508,416,578,602,652,650,814,698,932,870,994,1058,1124,1017,

%U 1334,1334,1408,1328,1642,1478,1808,1722,1806,1982,2164,1882,2306,2256,2452

%N a(n) = Sum_{k=0..n} n^notdivides(k, n), where notdivides(k, n) = 0 if k divides n, otherwise 1.

%H Peter Luschny, <a href="/A363735/b363735.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (1 - n) * tau(n) + n * (1 + n) for n >= 1, where tau = A000005.

%F a(n) + A363734(n) = (n + 1)^2.

%F a(n) - A363734(n) = A363421(n).

%t A363735[n_]:=If[n==0,1,n(n+1)+(1-n)DivisorSigma[0,n]];Array[A363735,100,0] (* _Paolo Xausa_, Aug 06 2023 *)

%o (SageMath)

%o print([sum(n^(not k.divides(n)) for k in srange(n + 1)) for n in srange(52)])

%o (Python)

%o from sympy import divisor_count

%o def A363735(n): return n*(n+1)-(n-1)*divisor_count(n) if n else 1 # _Chai Wah Wu_, Jun 28 2023

%Y Cf. A113704, A000005, A363734, A363421.

%K nonn

%O 0,2

%A _Peter Luschny_, Jun 27 2023